generalized conformal pseudo galilean algebras and their casimir operators a generalization of the conformal galilei algebra with levi subalgebra isomorphic to is introduced and a virtual copy of the latter in the enveloping algebra of the extension is constructed explicit expressions for the casimir operators are obtained from the determinant of polynomial matrices for the central factor algebra an exact formula giving the number of invariants is obtained and a procedure to compute invariant functions that do not depend on the variables of the levi subalgebra is developed it is further shown that such solutions determine complete sets of invariants provided that the relation is satisfied

n dimensional superintegrable systems from symplectic realizations of lie coalgebras the construction of n dimensional nd integrable systems from coalgebras is reviewed in the case of poisson coalgebras a necessary condition for the integrability of the nd coalgebra hamiltonian coming from a given coalgebra is obtained in terms of the dimension of the symplectic realization and the number of nonlinear casimir functions from this viewpoint the full set of three four and five dimensional lie poisson coalgebras is analysed and many new families of multiparametric nd integrable systems coming from the cases that fulfil the integrability condition are obtained including the explicit form of the integrals of the motion the superintegrability of these hamiltonians is also emphasized and the generalization of the whole construction to the quantum mechanical case is straightforward

an algorithm to calculate the invariants of any lie algebra an analytical method to calculate invariants is developed based on the theory of complete systems of simultaneous linear first order partial differential equations the application of this algorithm to the general case in which the invariants are not polynomials is included for the case of lie algebras with one invariant the procedure of finding the invariant can be computerized as an example of this procedure the algorithm is applied in the calculation of the invariants of the group sa n r the explicit construction of its invariants for n 2 3 4 is given a theorem determining the order of a polynomial invariant of a lie group is proven allowing us to show that the invariant of sa n r is a homogeneous polynomial of order 1 2n n 1 in the generators from this fact an immediate consequence is that the order in the generators of translations is n the method is also applied in the calculation of invariants of the dimension six solvable lie algebras and dimension seven nilpotent

generalized adaptive notch smoothers for real valued signals and systems systems with quasi periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters ganfs ganf algorithms can be considered an extension to the system case of classical adaptive notch filters anfs we show that estimation accuracy of the existing algorithms as well as their robustness to the choice of design parameters can be considerably improved by means of compensating estimation delay effects which occur in the amplitude tracking and frequency tracking loops of ganf anf filters apart from the increased computational burden the price for the achieved improvements is paid in terms of a decision delay the proposed generalized adaptive notch smoothing gans algorithms must be run on delayed input output data sequences since such delay is acceptable in many signal processing and system identification applications the proposed solution seems to be an attractive alternative to the currently available trackers

a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

orbit equivalence rigidity consider a countable group acting ergodically by measure p reserving transformations on a probability space x and let r be the corresponding orbit equivalence relation on x the following rigidity phenomenon is shown there exist group actions such that the equivalence relation r on x determines the group and the action x uniquely up to finite groups the natural action of sln z on the n torus r n z n for n 2 is one of such examples the interpretation of these results in the context of von neumann algebras provides some support to the conjecture of connes on rigidity of group algebras for groups with property t our rigidity results also give examples of countable equivalence relations of type ii1 which cannot be generated mod 0 by a free action of any group this gives a negative answer to a long standing problem of feldman and moore

two algorithms for adaptive retrieval of slowly time varying multiple cisoids in noise two algorithms for tracking parameters of slowly varying multiple complex sine waves cisoids in noise the multiple frequency tracker and the adaptive notch filter are described for high signal to noise ratio snr the properties of the algorithms i e stability noise rejection and tracking speed are studied analytically using a linear filter approximation technique the tradeoff between noise rejection and tracking error for both algorithms is shown to be similar different choices of the design variables are discussed namely i minimal mean square estimation error for random walk modeled frequency variations and ii minimal stationary estimation variance subject to a given tracking delay

some prime factorization results for type ii1 factors we prove several unique prime factorization results for tensor products of type ii1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected lie groups of real rank 1 in particular we show that if mathcal r overline otimes mathcal l mathbb f r 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f r m is isomorphic to a subfactor in mathcal r overline otimes mathcal l mathbb f s 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f s n for some 2 ri sj then m n

non solvable contractions of semisimple lie algebras in low dimension the problem of non solvable contractions of lie algebras is analysed by means of a stability theorem the problem is shown to be deeply related to the embeddings among semisimple lie algebras and the resulting branching rules for representations with this procedure we determine all deformations of indecomposable lie algebras having a nontrivial levi decomposition onto semisimple lie algebras of dimension n 8 and obtain the non solvable contractions of the latter class of algebras

orbit inequivalent actions for groups containing a copy of mathbb f _ 2 we prove that if a countable group contains a copy of mathbb f 2 then it admits uncountably many non orbit equivalent actions

fundamental group of uniquely ergodic cantor minimal systems abstract we introduce the fundamental group f r g of a uniquely ergodic cantor minimal g system r g where g is a countable discrete group we compute fundamental groups of several uniquely ergodic cantor minimal g systems we show that if r g arises from a free action of a finitely generated abelian group then there exists a unital countable subring r of r such that f r g r we also consider the relation between fundamental groups of uniquely ergodic cantor minimal z n systems and fundamental groups of crossed product c algebras c x z n

determinantal formulae for the casimir operators of inhomogeneous lie algebras the author would like to correct some inaccuracy in formula 6 please see pdf for details

some oe and w rigidity results for actions by wreath product groups we use deformation rigidity theory in the von neumann algebra framework to study probability measure preserving actions by wreath product groups in particular we single out large families of wreath product groups satisfying various types of orbit equivalence oe rigidity for instance we show that whenever h k are icc property t groups such that h and k admit stably orbit equivalent action and such that h and k are ergodic then automatically is stably orbit equivalent to and h is stably orbit equivalent to k rigidity results for von neumann algebras arising from certain actions of such groups i e w rigidity results are also obtained

orbit equivalence rigidity and bounded cohomology we establish new results and introduce new methods in the theory of measurable orbit equivalence using bounded cohomology of group representations our rigidity statements hold for a wide uncountable class of groups arising from negative curvature geometry amongst our applications are a measurable mostow type rigidity theorems for products of negatively curved groups b prime factorization results for measure equivalence c superrigidity for orbit equivalence d the first examples of continua of type ii1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic

identification of quasi periodically varying systems using the combined nonparametric parametric approach the problem of identification of quasi periodically varying finite impulse response systems is considered neither the number of system frequency modes nor the initial frequency values are assumed to be known a priori the proposed solution is a blend of the parametric model based and nonparametric discrete fourier transform based approach to system identification it is shown that the results of nonparametric analysis can be used to identify the number of frequency modes and to determine initial conditions needed to smoothly start or restart the model based tracking algorithm such a combined nonparametric parametric approach allows one to preserve advantages of both frameworks leading to an estimation procedure which guarantees global frequency search high frequency resolution fast initial convergence and good steady state tracking capabilities

weak exactness for c algebras and application to condition ao abstract kirchberg introduced weak exactness for von neumann algebras as an analogue of exactness for c algebras ozawa found useful characterizations of weak exactness and he proved that weak exactness for group von neumann algebras is equivalent to exactness of the groups we generalize this concept to inclusions of c algebras in von neumann algebras and study some fundamental properties and relationship to kirchberg s weak exactness we then give some permanence properties which are similar to those of exact groups in the last section we study a similar condition to ozawa s condition ao with our weak exactness and generalize ozawa s theorem for bi exact groups as a corollary we give new examples of prime factors

a converse to dye s theorem every non amenable countable group induces orbit inequivalent ergodic equivalence relations on standard borel probability spaces not every free ergodic measure preserving action of f 2 on a standard borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces there is a treeable non hyperfinite borel equivalence relation which is not universal for treeable in the b ordering

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

the casimir operators of inhomogeneous groups we have found the number of invariant operators for the inhomogeneous groups igl n r isl n r iso p q iu p q isu p q isp 2n i e the inhomogeneous groups with the classical homogeneous subgroups and also for the weyl group w p q for some special cases explicit forms of the invariant operators are obtained we also discuss the methods applied together with problems in some cases possible further developments and relevance for the supersymmetric theories

all solvable extensions of a class of nilpotent lie algebras of dimension n and degree of nilpotency n 1 we construct all solvable lie algebras with a specific n dimensional nilradical of degree of nilpotency n 1 and with an n 2 dimensional maximal abelian ideal we find that for given n such a solvable algebra is unique up to isomorphisms using the method of moving frames we construct a basis for the casimir invariants of the nilradical we also construct a basis for the generalized casimir invariants of its solvable extension consisting entirely of rational functions of the chosen invariants of the nilradical

product groups acting on manifolds we analyse volume preserving actions of product groups on riemannian manifolds under a natural spectral irreducibility assumption we prove the following dichotomy either the action is measurably isometric in which case there are at most two factors or the action is infinitesimally linear which means that the derivative cocycle arises from unbounded linear representations of all factors as a first application this provides lower bounds on the dimension of the manifold in terms of the number of factors in the acting group another application is a strong restriction for actions of non linear groups we prove our results by means of a new cocycle superrigidity theorem of independent interest in analogy to zimmer s programme

one cohomology and the uniqueness of the group measure space decomposition of a ii1 factor we provide a unified and self contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a ii1 factor we single out a large class of groups characterized by a one cohomology property and prove that for every free ergodic probability measure preserving action of the associated ii1 factor has a unique group measure space cartan subalgebra up to unitary conjugacy our methods follow closely a recent article of chifan peterson but we replace the usage of peterson s unbounded derivations by thomas sinclair s dilation into a malleable deformation by a one parameter group of automorphisms

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

superrigidity for irreducible lattices and geometric splitting we prove general superrigidity results for actions of irreducible lattices on cat 0 spaces first in terms of the ideal boundary and then for the intrinsic geometry including for infinite dimensional spaces in particular one obtains a new and self contained proof of margulis superrigidity theorem for uniform irreducible lattices in non simple groups the proofs rely on simple geometric arguments including a splitting theorem which can be viewed as an infinite dimensional and singular generalization of the lawson yau gromoll wolf theorem appendix a gives a very elementary proof of commensurator superrigidity appendix b proves that all our results also hold for certain non uniform lattices

contractions of invariants of lie algebras with applications to classical inhomogeneous lie algebras we study in full generality the contraction of invariants of finite dimensional lie algebras and give some illustrative examples our applications show that the contraction method is not only quite flexible but also has the advantage over other methods that independent invariants can be contracted into independent ones and that they appear in compact tensorial form for our applications of physical interest we can restrict ourselves to polynomial invariants casimir operators and generalized inonu wigner contractions we show how to get all invariants of the inhomogeneous lie algebras iso p q iu p q isl n r and isp 2n r from those of the homogeneous lie algebras these invariants are all known but our results for isl n r and isp 2n r appear in a much more desirable form

virtual copies of semisimple lie algebras in enveloping algebras of semidirect products and casimir operators given a semidirect product g s r of semisimple lie algebras s and solvable algebras r we construct polynomial operators in the enveloping algebra u g of g that commute with r and transform like the generators of s up to a functional factor that turns out to be a casimir operator of r such operators are said to generate a virtual copy of s in u g and allow to compute the casimir operators of g in closed form using the classical formulae for the invariants of s the behavior of virtual copies with respect to contractions of lie algebras is analyzed applications to the class of hamilton algebras and their inhomogeneous extensions are given

strongly solid group factors which are not interpolated free group factors we give examples of non amenable infinite conjugacy classes groups with the haagerup property weakly amenable with constant cb 1 for which we show that the associated ii1 factors l are strongly solid i e the normalizer of any diffuse amenable subalgebra p subset l gamma generates an amenable von neumann algebra nevertheless for these examples of groups l is not isomorphic to any interpolated free group factor l ft for 1 t

integrable measure equivalence and rigidity of hyperbolic lattices we study rigidity properties of lattices in operatorname isom mathbf h n simeq mathrm so n 1 mathbb r n 3 and of surface groups in operatorname isom mathbf h 2 simeq mathrm sl 2 mathbb r in the context of integrable measure equivalence the results for lattices in operatorname isom mathbf h n n 3 are generalizations of mostow rigidity they include a cocycle version of strong rigidity and an integrable measure equivalence classification despite the lack of mostow rigidity for n 2 we show that cocompact lattices in operatorname isom mathbf h 2 allow a similar integrable measure equivalence classification

non semisimple lie algebras with levi factor fraktur so 3 fraktur sfraktur l 2 bbb r and their invariants we analyse the number of functionally independent generalized casimir invariants for non semisimple lie algebras r with levi factors isomorphic to 3 and 2 in dependence of the pair r formed by a representation r of and a solvable lie algebra we show that for any dimension n 6 there exist lie algebras r with non trivial levi decomposition such that r 0

internal labelling operators and contractions of lie algebras we analyse under which conditions the missing label problem associated with a reduction chain of simple lie algebras can be completely solved by means of an inonu wigner contraction naturally related to the embedding this provides a new interpretation of the missing label operators in terms of the casimir operators of the contracted algebra and shows that the available labelling operators are not completely equivalent further the procedure is used to obtain upper bounds for the number of invariants of affine lie algebras arising as contractions of semi simple algebras

a class of ii1 factors with many non conjugate cartan subalgebras abstract we construct a class of ii 1 factors m that admit unclassifiably many cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of m is complete analytic in particular non borel we also construct a ii 1 factor that admits uncountably many non isomorphic group measure space decompositions all involving the same group g so g is a group that admits uncountably many non stably orbit equivalent actions whose crossed product ii 1 factors are all isomorphic

unique cartan decomposition for ii1 factors arising from arbitrary actions of free groups we prove that for any free ergodic probability measure preserving action mathbb f n curvearrowright x mu of a free group on n generators mathbb f n 2 leq n leq infty the associated group measure space ii1 factor l infty x rtimes mathbb f n has l x as its unique cartan subalgebra up to unitary conjugacy we deduce that group measure space ii1 factors arising from actions of free groups with different number of generators are never isomorphic we actually prove unique cartan decomposition results for ii1 factors arising from arbitrary actions of a much larger family of groups including all free products of amenable groups and their direct products

cout des relations d equivalence et des groupes we study a new dynamical invariant for dicrete groups the cost it is a real number in 1 1 n 1 bounded by the number of generators of the group and it is well behaved with respect to finite index subgroups namely the quantities 1 minus the cost are related by multiplying by the index the cost of every infinite amenable group equals 1 we compute it in some other situations including free products free products with amalgamation and hnn extensions over amenable groups and for direct product situations for instance the cost of the free group on n generators equals n we prove that each possible finite value of the cost is achieved by a finitely generated group it is dynamical because it relies on measure preserving free actions on probability borel spaces in most cases groups have fixed price which implies that two freely acting groups which define the same orbit partition must have the same cost it enables us to distinguish the orbit partitions of probability preserving free actions of free groups of different ranks at the end of the paper we give a mercuriale i e a list of costs of different groups the cost is in fact an invariant of ergodic measure preserving equivalence relations and is defined using graphings a treeing is a measurable way to provide every equivalence class orbit with the structure of a simplicial tree this an example of graphing not every relation admits a treeing we prove that every free action of a cost 1 non amenable group is not treeable but we prove that subrelations of treeable relations are treeable we give examples of relations which cannot be produced by an action of any finitely generated group the cost of a relation which can be decomposed as a direct product is shown to be 1 we define the notion for a relation to be a free product or an hnn extension and compute the cost for the resulting relation from the costs of the building blocks the cost is also an invariant of the pairs von neumann algebra cartan subalgebra

generalized adaptive notch smoothing revisited the problem of identification of quasi periodically varying dynamic systems is considered this problem can be solved using generalized adaptive notch filtering ganf algorithms it is shown that the accuracy of parameter estimates can be significantly increased if the results obtained from ganf are further processed using a cascade of appropriately designed filters the resulting generalized adaptive notch smoothing gans algorithm can be employed in many off line or nearly real time on line applications such as elimination of sinusoidal interference from a prerecorded signal or identification of a rapidly varying telecommunication channel

measure equivalence rigidity and bi exactness of groups we get three types of results on measurable group theory direct product groups of ozawa s class s groups wreath product groups and amalgamated free products we prove measure equivalence factorization results on direct product groups of ozawa s class s groups as consequences monod shalom type orbit equivalence rigidity theorems follow we prove that if two wreath product groups a g b of non amenable exact direct product groups g with amenable bases a b are measure equivalent then g and are measure equivalent we get bass serre rigidity results on amalgamated free products of non amenable exact direct product groups

actions of _ whose ii factors and orbit equivalence relations have prescribed fundamental group we show that given any subgroup f of r which is either countable or belongs to a certain large class of uncountable subgroups there exist continuously many free ergodic measure preserving actions i of the free group with infinitely many generators f1 on probability measure spaces xi i such that their associated group measure space ii1 factors mi l 1 xi o i f1 and orbit equivalence relationsri r f1 y xi have fundamental group equal tof and with mi respectivelyri stably non isomorphic moreover these actions can be taken so thatri has no outer automorphisms and any automorphism of mi is unitary conjugate to an automorphism that acts trivially on the subalgebra l 1 xi of mi

continuous cocycle superrigidity for shifts and groups with one end we prove that if a finitely generated group g is not torsion then a necessary and sufficient condition for every full shift over g has continuous cocycle superrigidity is that g has one end it is a topological version of the well known popa s measurable cocycle superrigidity theorem cocycle and orbit equivalence superrigidity for malleable actions of w rigid groups invent math 170 2 243 295 2007 for the proof of sufficiency we introduce a new specification property for shifts over general groups which plays a similar role as malleable property in the measurable setting this new specification property is good enough for us to extend the method of using homoclinic equivalence relation that was introduced by schmidt pac j math 170 1 237 269 1995 to study cocycle rigidity for mathbb z d shifts indeed in this direction we prove this superrigidity result for certain more general systems and for the necessary condition we apply specker s characterization for ends of groups via the associated first cohomology groups to get the result finally combining our results with li ergod theory dyn syst arxiv 1503 01704 theorem 1 6 we have an application in continuous orbit equivalence rigidity

classification of type iii bernoulli crossed products abstract crossed products with noncommutative bernoulli actions were introduced by connes as the first examples of full factors of type i i i this article provides a complete classification of the factors p f n f n where f n is the free group and p is an amenable factor with an almost periodic state we show that these factors are completely classified by the rank n of the free group f n and connes s sd invariant we prove similar results for free product groups as well as for classes of generalized bernoulli actions

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

oe and w superrigidity results for actions by surface braid groups we show that several important normal subgroups of the mapping class group of a surface satisfy the following property any free ergodic probability measure preserving action y x is stablyoe superrigid these include the central quotients of most surface braid groups and most torelli groups and johnson kernels in addition we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice embeddings using these results in combination with previous results from cik13 we deduce that any free ergodic probabilitymeasure preserving action of almost any surface braid group is stablyw superrigid i e it can be completely reconstructed from its vonneumann algebra

asymptotic structure of free araki woods factors the purpose of this paper is to investigate the structure of shlyakhtenko s free araki woods factors using the framework of ultraproduct von neumann algebras we first prove that all the free araki woods factors gamma h mathbb r u t prime prime are omega solid in the following sense for every von neumann subalgebra q subset gamma h mathbb r u t prime prime that is the range of a faithful normal conditional expectation and such that the relative commutant q cap m omega is diffuse we have that q is amenable next we prove that the continuous cores of the free araki woods factors gamma h mathbb r u t prime prime associated with mixing orthogonal representations u mathbb r rightarrow mathcal o h mathbb r are omega solid type mathrm ii infty factors finally when the orthogonal representation u mathbb r rightarrow mathcal o h mathbb r is weakly mixing we prove a dichotomy result for all the von neumann subalgebras q subset gamma h mathbb r u t prime prime that are globally invariant under the modular automorphism group sigma t varphi u of the free quasi free state varphi u

compact actions and uniqueness of the group measure space decomposition of ii1 factors abstract we prove that any ii1 factor l x arising from a compact free ergodic probability measure preserving action of a countable group with positive first l 2 betti number 1 2 0 has a unique group measure space cartan subalgebra up to unitary conjugacy

relative property t for the subequivalence relations induced by the action of sl2 z on t2 abstract let s be the equivalence relation induced by the action sl 2 z t 2 2 where 2 denotes the haar measure on the 2 torus t 2 we prove that any ergodic subequivalence relation r of s is either hyperfinite or rigid in the sense of s popa 41 the proof uses an ergodic theoretic criterion for rigidity of countable ergodic probability measure preserving equivalence relations moreover we give a purely ergodic theoretic formulation of rigidity for free ergodic probability measure preserving actions of countable groups

on tracking properties of real valued generalized adaptive notch filters generalized adaptive notch filters ganfs are used for identification tracking of quasi periodically varying dynamic systems and can be considered an extension to the system case of classical adaptive notch filters the paper presents results of local performance analysis of a real valued ganf algorithm i e algorithm designed to track parameters of a real valued system this is an extension of the previous work which focused on complex valued systems tracking properties of the algorithm are studied analytically using an approximating linear filter technique and an averaging approach even though restricted to a single frequency case the presented analysis provides interesting insights into the tracking mechanisms of ganf and allows one to formulate some useful rules of thumb for choosing design parameters

central extensions of the families of quasi unitary lie algebras the most general possible central extensions of two whole families of lie algebras which can be obtained by contracting the special pseudo unitary algebras of the cartan series and the pseudo unitary algebras are completely determined and classified for arbitrary p and q in addition to the and algebras whose second cohomology group is well known to be trivial each family includes many non semisimple algebras their central extensions which are explicitly given can be classified into three types as far as their properties under contraction are involved a closed expression for the dimension of the second cohomology group of any member of these families of algebras is given

tracking analysis of a generalized adaptive notch filter the paper presents results of local performance analysis of a generalized adaptive notch filter ganf ganfs are used for identification tracking of quasi periodically varying dynamic systems and can be considered an extension to the system case of classical adaptive notch filters the tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique even though restricted to a single frequency case the presented analysis provides valuable insights into the tracking mechanisms of ganf including the associated speed accuracy tradeoffs the achievable performance bounds and tracking limitations in addition it allows one to formulate some useful rules of thumb for choosing design parameters

some rigidity results for non commutative bernoulli shifts abstract we introduce the outer conjugacy invariants s s s for cocycle actions of discrete groups g on type ii 1 factors n as the set of real numbers t 0 for which the amplification t of can be perturbed to an action respectively to a weakly mixing action we calculate explicitly s s s and the fundamental group of f in the case g has infinite normal subgroups with the relative property t e g when g itself has the property t of kazhdan and is an action of g on the hyperfinite ii 1 factor by connes stormer bernoulli shifts of weights t i i thus s s and f coincide with the multiplicative subgroup s of r generated by the ratios t i t j i j while s z if s 1 i e when all weights are equal and s r otherwise in fact we calculate all the 1 cohomology picture of t t 0 and classify the actions g in terms of their weights t i i in particular we show that any 1 cocycle for g vanishes modulo scalars and that two such actions are cocycle conjugate iff they are conjugate also any cocycle action obtained by reducing a bernoulli action of a group g as above on n g g m n n c tr g to the algebra pnp for p a projection in n p 0 1 cannot be perturbed to a genuine action

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

generalized adaptive notch and comb filters for identification of quasi periodically varying systems the problem of identification tracking of quasi periodically varying real valued systems is considered this problem is a generalization to the system case of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise the solution is based on the exponentially weighted basis function ewbf approach the proposed algorithms are capable of tracking slow changes in system frequencies which means that not only the expansion coefficients in the basis function description of the analyzed system but also the basis functions themselves are adjusted in an adaptive manner first assuming that the system frequencies are known and constant the running basis and fixed basis variants of the ewbf algorithm are derived and their relationship to the classical notch filter with constrained poles and zeros is established next the frequency adaptive versions of both algorithms are obtained using the gradient search and recursive prediction error principles respectively finally the interrelated frequencies case is analyzed and two additional parameter tracking algorithms generalized adaptive comb filters are derived

casimir invariants for the complete family of quasisimple orthogonal algebras a complete choice of generators of the centre of the enveloping algebras of real quasisimple lie algebras of orthogonal type for arbitrary dimension is obtained in a unified setting the results simultaneously include the well known polynomial invariants of the pseudo orthogonal algebras as well as the casimirs for many non simple algebras such as the inhomogeneous the newton hooke and galilei type etc which are obtained by contraction s starting from the simple algebras the dimension of the centre of the enveloping algebra of a quasisimple orthogonal algebra turns out to be the same as for the simple algebras from which they come by contraction the structure of the higher order invariants is given in a convenient pyramidal manner in terms of certain sets of pauli lubanski elements in the enveloping algebras as an example showing this approach at work the scheme is applied to recovering the casimirs for the 3 1 kinematical algebras some prospects on the relevance of these results for the study of expansions are also given

strong solidity of group factors from lattices in so n 1 and su n 1 abstract we show that the group factors l where is an icc lattice in either so n 1 or su n 1 n 2 are strongly solid in the sense of ozawa and popa 2010 13 this strengthens a result of ozawa and popa 2010 14 showing that these factors do not have cartan subalgebras

a remark on t valued cohomology groups of algebraic group actions we prove that for a weakly mixing algebraic action g x the nth cohomology group hn g x t after quotienting out the natural subgroup hn g t contains hn g x as a natural subgroup for n 1 if we further assume the diagonal actions 2 4 are t cocycle superrigid and h2 g x is torsion free as an abelian group then the above also holds true for n 2 applying it for principal algebraic actions when n 1 we show that h2 g zg is torsion free as an abelian group when g has property t as a direct corollary of sorin popa s cocycle superrigidity theorem we also use it when n 2 to answer negatively a question of sorin popa on the 2nd cohomology group of bernoulli shift actions of property t groups