isotropic random walks in a building of type let d 1 be an integer and let be a locally finite thick building of type when d 1 is a tree which we assume is homogeneous and a transition probability matrix p or the corresponding random walk on the vertex set of is called isotropic if for any vertices x y p x y depends only on the graph distance from x to y in this paper we extend the definition of isotropic to general d in a natural way and study isotropic random walks zn on the vertex set of in particular we prove a rate of escape theorem with an explicit formula for we prove a central limit theorem and a local limit theorem these generalize results of sawyer 21 in the case d 1 we do not need to assume that eq1 is obtained from a local field f by the standard construction but in that case our results may be translated into theorems about bi k invariant probability measures on groups such as pgl d 1 f and sl d 1 f which act on eq1

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

hyperinvariant subspaces for some b circular operators we show that if a is a hilbert space operator then the set of all projections onto hyperinvariant subspaces of a which is contained in the von neumann algebra n a that is generated by a is independent of the representation of n a thought of as an abstract w algebra we modify a technique of foias ko jung and pearcy to get a method for finding nontrivial hyperinvariant subspaces of certain operators in finite von neumann algebras we introduce the b circular operators as a special case of speicher s b gaussian operators in free probability theory and we prove several results about a b circular operator z including formulas for the b valued cauchy and r transforms of z z we show that a large class of l 0 1 circular operators in finite von neumann algebras have nontrivial hyperinvariant subspaces and that another large class of them can be embedded in the free group factor l f3 these results generalize some of what is known about the quasinilpotent dt operator

higher homotopy operations and andre quillen cohomology there are two main approaches to the problem of realizing a algebra a graded group equipped with an action of the primary homotopy operations as the homotopy groups of a space x both involve trying to realize an algebraic free simplicial resolution g of by a simplicial space w and proceed by induction on the simplicial dimension the first provides a sequence of andre quillen cohomology classes in hn 2 n n 1 as obstructions to the existence of successive postnikov sections for w cf dwyer et al 1995 27 the second gives a sequence of geometrically defined higher homotopy operations as the obstructions cf blanc 1995 8 these were identified in blanc et al 2010 16 with the obstruction theory of dwyer et al 1989 25 there are also algebraic and geometric obstructions for distinguishing between different realizations of in this paper we a provide an explicit construction of the cocycles representing the cohomology obstructions b provide a similar explicit construction of certain minimal values of the higher homotopy operations which reduce to long toda brackets and c show that these two constructions correspond under an evident map

singular perturbation method for initial value problems with inputs in discrete control systems abstract a linear time invariant singularly perturbed initial value problem with input arising in discrete control systems is considered a singular perturbation method is developed to solve an inhomogeneous difference equation in classical form containing several small parameters the same is dealt with in state space form also and the advantage of this approach is clearly brought out the method is demonstrated by a numerical example

deconstructing hopf spaces we characterize hopf spaces with finitely generated cohomology as an algebra over the steenrod algebra we deconstruct the original space into an h space y with finite mod p cohomology and a finite number of p torsion eilenberg mac lane spaces we give a precise description of homotopy commutative h spaces in this setting

unitary representations of affine hecke algebras related to macdonald spherical functions abstract for any reduced crystallographic root system we introduce a unitary representation of the extended affine hecke algebra given by discrete difference reflection operators acting in a hilbert space of complex functions on the weight lattice it is shown that the action of the center under this representation is diagonal on the basis of macdonald spherical functions as an application we compute an explicit pieri formula for these spherical functions

on the matrix riccati equation for a singularly perturbed linear discrete control system abstract a difference approximation to a singularly perturbed linear time varying continuous time control system is presented and is called a singularly perturbed linear discrete time control system under several assumptions it is shown that the riccati equation for the reduced system in the sense of singular perturbation agrees with that for the associated subsystem of the full non reduced system when a small parameter in the equation is set zero on the basis of this result it is also shown that the optimal controls and the corresponding trajectories for the two systems are consistent with each other when a small parameter for the full system is set zero

buildings and hecke algebras abstract in this paper we establish a strong connection between buildings and hecke algebras by studying two algebras of averaging operators on buildings to each locally finite regular building we associate a natural algebra b of chamber set averaging operators and when the building is affine we also define an algebra a of vertex set averaging operators we show that for appropriately parametrised hecke algebras h and h the algebra b is isomorphic to h and the algebra a is isomorphic to the centre of h on the one hand these results give a thorough understanding of the algebras a and b on the other hand they give a nice geometric and combinatorial understanding of hecke algebras and in particular of the macdonald spherical functions and the centre of affine hecke algebras our results also produce interesting examples of association schemes and polynomial hypergroups in later work we use the results here to study random walks on affine buildings

spherical harmonic analysis on affine buildings let be a locally finite regular affine building with root system r there is a commutative algebra spanned by averaging operators a p acting on the space of all functions f v p where v p is in most cases the set of all special vertices of and p is a set of dominant coweights of r this algebra is studied in 6 and 7 for a n buildings and the general case is treated in 15 in this paper we show that all algebra homomorphisms h may be expressed in terms of the macdonald spherical functions we also provide a second formula for these homomorphisms in terms of an integral over the boundary of we may regard as a subalgebra of the c algebra of bounded linear operators on l2 v p and we write for the closure of in this algebra we study the gelfand map where m2 and we compute m2 and the plancherel measure of we also compute the l2 operator norms of the operators a p in terms of the macdonald spherical functions

on the symmetric enveloping algebra of planar algebra subfactors we give a diagrammatic description of popa s symmetric enveloping algebras associated to planar algebra subfactors as an application we construct a natural family of derivations on these factors and compute a certain free entropy dimension type quantity 2013 american mathematical society

factoriality of hecke von neumann algebras of right angled coxeter groups abstract the hecke algebra c q w of a coxeter group w associated to parameter q can be completed to a von neumann algebra n q w we study such algebras in case where w is right angled we determine the range of q for which n q w is a factor i e has trivial center moreover in case of nontrivial center we prove a result allowing to decompose n q w into a finite direct sum of factors

limit laws for random matrices and free products in earlier articles we studied a kind of probability theory in the framework of operator algebras with the tensor product replaced by the free product we prove here that free random variables naturally arise as limits of random matrices and that wigner s semicircle law is a consequence of the central limit theorem for free random variables in this way we obtain a non commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra wigner s law being given by the trace of the spectral measure of the selfadjoint component of this operator

free entropy dimension in amalgamated free products we calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von neumann algebras with amalgamation over a hyperfinite subalgebra in particular some exotic popa algebra generators of free group factors are shown to have the expected free entropy dimension we also show that microstates and non microstates free entropy dimension agree for generating sets of many groups in the appendix the first l 2 betti number for certain amalgamated free products of groups is calculated

on topologically realizing modules over the steenrod algebra the mod p cohomology of a space or spectrum x is a module over the mod p steenrod algebra a if x is a space it has additional structure making it an unstable a algebra where we recall that an a module m is unstable if when p 2 sqi x 0 for all i ixi and x e m and when p 2 3epix 0 for all 2i e jxj e 0 or 1 and x e m questions about realizing particular a modules algebras and a algebras as the cohomology of spaces or spectra are among the most fundamental in algebraic topology the hopf invariant one problem a and the problem of realizing polynomial algebras dmw are two famous examples of ongoing interest if one regards the first of these as a problem about realizing finite a modules and the second of these as a problem about realizing rather large a modules it is the purpose of this paper to study the middle ground we begin with the following conjecture

hecke algebras from groups acting on trees and hnn extensions abstract we study hecke algebras of groups acting on trees with respect to geometrically defined subgroups in particular we consider hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and the stabilizer of an end relative to a vertex stabilizer assuming that the actions are sufficiently transitive we focus on identifying the structure of the resulting hecke algebras give explicit multiplication tables of the canonical generators and determine whether the hecke algebra has a universal c completion the paper unifies algebraic and analytic approaches by focusing on the common geometric thread the results have implications for the general theory of totally disconnected locally compact groups

free subproducts and free scaled products of ii1 factors abstract the constructions of free subproducts of von neumann algebras and free scaled products are introduced and results about them are proved including rescaling results and results about free trade in free scaled products

the hall polynomial revisited abstract the hall polynomial g p counts subgroups of type and cotype in a finite abelian p group of type we derive a formula for g p along the lines of t klein s original formula but much simpler which shows that its expansion in powers of p 1 has nonnegative coefficients

singular perturbation modelling of continuous and discrete physical systems the major shortcoming of the singular perturbation theory preventing its application to practical problems is that the system described by state equations is seldom given in the singularly perturbed form this paper presents a systematic procedure which converts the state equations of a large scale time invariant system to singularly perturbed form assuming that such a classification is possible this is accomplished by appropriate scaling and grouping of the state variables into slow and fast groups while retaining as many physical state variables as possible in the new state description an improved slow fast grouping of the states can result by allowing linear combination of certain available physical variables as new state variables several examples are given to illustrate the method

singular perturbation modelling of large scale systems with multi time scale property the problem is investigated of singular perturbation modelling which plays an important role in cases of the application of the singular perturbation method to the design and analysis of large scale systems in both continuous and discrete time versions modelling concepts based on structural properties are studied and computer oriented algorithms are developed the results of two time scale systems are extended to multi time scale cases furthermore in order to verify the validity of these studies some numerical examples are given

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods

guionnet jones shlyakhtenko subfactors associated to finite dimensional kac algebras abstract we analyse the guionnet jones shlyakhtenko construction for the planar algebra associated to a finite dimensional kac algebra and identify the factors that arise as finite interpolated free group factors

dynamic condensation method for structural eigenvalue analysis an improved dynamic condensation approach is presented for accurate calculation of structural eigenproperties the approach is iterative the kept and reduced degrees of freedom in the approach are related through a condensation matrix that is used to form a condensed eigenvalue problem an initial condensation matrix can be defined in terms of the system submatrices the eigenproperties calculated in an iterative step are utilized to update the condensation matrix matrix inversions or gaussian eliminations are avoided in the updating process by employing the orthogonality of the eigenvectors the process of updating the condensation matrix and the eigenvalue problem is repeated until a desired convergence in the eigenvalues is achieved usually a few iterations are quite adequate iterations for both the lower as well as the higher modes can be performed as the condensation matrices for the two sets of modes are very simply related numerical examples are presented to show the applicability of the proposed approach several methods that have been used in practice to select the kept degrees of freedom for condensing are also evaluated numerically with respect to their effectiveness in providing accurate estimates of the eigenproperties with a minimum number of iterations

on the guionnet jones shlyakhtenko construction for graphs abstract using an analogue of the guionnet jones shlyakhtenko construction for graphs we show that their construction applied to any subfactor planar algebra of finite depth yields an inclusion of interpolated free group factors with finite parameter thereby giving another proof of their universality for finite depth planar algebras

compressions of free products of von neumann algebras a reduction formula for compressions of von neumann algebra ii 1 factors arising as free products is proved this shows that the fundamental group is bf r for some such algebras additionally by taking a sort of free product with an unbounded semicircular element continuous one parameter groups of trace scaling automorphisms on ii infty factors are constructed this produces type iii 1 factors with core mathcal m otimes b mathcal h where mathcal m can be a full ii 1 factor without the haagerup approximation property

a classification of commutative parabolic hecke algebras let w s be a coxeter system with i s such that the parabolic subgroup wi is finite associated to this data there is a hecke algebra h and a parabolic hecke algebra hi 1ih1i over a ring z qs s s we give a complete classification of the commutative parabolic hecke algebras across all coxeter types

higher homotopy operations we provide a general definition of higher homotopy operations encompassing most known cases including higher massey and whitehead products and long toda brackets these operations are defined in terms of the w construction of boardman and vogt applied to the appropriate diagram category we also show how some classical families of polyhedra including simplices cubes associahedra and permutahedra arise in this way

on certain free product factors via an extended matrix model abstract a random matrix model for freeness is extended and used to investigate free products of free group factors with matrix algebras and with the hyperfinite ii 1 factor the latter is shown to be isomorphic to a free group factor having one additional generator

asymptotic entropy of random walks on fuchsian buildings and kac moody groups in this article we prove existence of the asymptotic entropy for isotropic random walks on regular fuchsian buildings moreover we give formulae for the asymptotic entropy and prove that it is equal to the rate of escape of the random walk with respect to the green distance when the building arises from a fuchsian kac moody group our results imply results for random walks induced by bi invariant measures on these groups however our results are proven in the general setting without the assumption of any group acting on the building the main idea is to consider the retraction of the isotropic random walk onto an apartment of the building to prove existence of the asymptotic entropy for this retracted walk and to lift this in order to deduce the existence of the entropy for the random walk on the building

a semi finite algebra associated to a subfactor planar algebra we canonically associate to any planar algebra two type ii factors m the subfactors constructed previously by the authors in guionnet et al 2010 6 are isomorphic to compressions of m to finite projections we show that each m is isomorphic to an amalgamated free product of type i von neumann algebras with amalgamation over a fixed discrete type i von neumann subalgebra in the finite depth case existing results in the literature imply that m m is the amplification a free group factor on a finite number of generators as an application we show that the factors mj constructed in guionnet et al in press 6 are isomorphic to interpolated free group factors l f rj rj 1 2 2j 1 i where 2 is the index of the planar algebra and i is its global index other applications include computations of laws of jones wenzl projections

the free entropy dimension of hyperfinite von neumann algebras suppose m is a hyperfinite von neumann algebra with a normal tracial state and 1 n is a set of selfadjoint generators for m we calculate 0 1 n the modified free entropy dimension of 1 n moreover we show that 0 1 n depends only on m and consequently 0 1 n is independent of the choice of generators for m in the course of the argument we show that if b 1 b n is a set of selfadjoint generators for a von neumann algebra r with a normal tracial state and b 1 b n has finite dimensional approximants then 0 n 0 b 1 b n for any hyperfinite von neumann subalgebra n of r combined with a result by voiculescu this implies that if r has a regular diffuse hyperfinite von neumann subalgebra then 0 b 1 b n 1

scale and tidy subgroups for weyl transitive automorphism groups of buildings abstract we consider closed weyl transitive groups of automorphisms of thick buildings for each element of such a group we derive a combinatorial formula for its scale and establish the existence of a tidy subgroup for it that equals the stabilizer of a simplex simplices whose stabilizers are tidy for some element of the group are characterized in terms of the minimal set of the isometry induced by the element on the davis realization of the building and in terms of the weyl distance between them and their image we use our results to derive some topological properties of closed weyl transitive groups of automorphisms

reduced free products of finite dimensional c algebras abstract we find a necessary and sufficient conditions for the simplicity and uniqueness of trace for reduced free products of finite families of finite dimensional c algebras with specified traces on them

rigidity results for wreath product ii1 factors abstract we consider ii 1 factors of the form m g b g where either i b is a non hyperfinite ii 1 factor and g is an icc amenable group or ii b is a weakly rigid ii 1 factor and g is icc group and where g acts on g b by bernoulli shifts we prove that isomorphism of two such factors implies cocycle conjugacy of the corresponding bernoulli shift actions in particular the groups acting must be isomorphic as a consequence we can distinguish between certain classes of group von neumann algebras associated to wreath product groups

mixing and weakly mixing abelian subalgebras of type ii1 factors abstract this paper studies weakly mixing singular and mixing masas in type ii 1 factors from a bimodule point of view several necessary and sufficient conditions characterizing the normalizing algebra of a masa are presented we study the structure of mixing inclusions with special attention paid to masas of product class a recent result of jolissaint and stalder concerning mixing masas arising out of inclusions of groups is revisited one consequence of our structural results rules out the existence of certain koopman realizable measures arising from semidirect products which are absolutely continuous but not lebesgue we also show that there exist uncountably many pairwise non conjugate mixing masas in the free group factors each with pukanszky invariant 1

geometric properties and invariant manifolds of the riccati equation this short paper considers the general riccati matrix differential equation it reviews and extends results on the characterization and existence of equilibrium solutions establishes that the riccati equation has at most one stable equilibrium solution as t rightarrow infty or t rightarrow infty and confines the region of attraction to this unique stable equilibrium solution by identifying and utilizing linear and nonlinear invariant manifolds of the riccati equation

distance regularity in buildings and structure constants in hecke algebras in this paper we define generalised spheres in buildings using the simplicial structure and weyl distance in the building and we derive an explicit formula for the cardinality of these spheres we prove a generalised notion of distance regularity in buildings and develop a combinatorial formula for the cardinalities of intersections of generalised spheres motivated by the classical study of algebras associated to distance regular graphs we investigate the algebras and modules of hecke operators arising from our generalised distance regularity and prove isomorphisms between these algebras and more well known parabolic hecke algebras we conclude with applications of our main results to non negativity of structure constants in parabolic hecke algebras commutativity of algebras of hecke operators double coset combinatorics in groups with bn pairs and random walks on the simplices of buildings

a hurewicz spectral sequence for homology for any connected space x and ring r we describe a first quadrant spectral sequence converging to h x r whose e2 term depends only on the homotopy groups of x and the action of the primary homotopy operations on them we show that for simply connected x the e2 term vanishes below a line of slope 1 2 computing part of the e2 term just above this line we find a certain periodicity which shows in particular that this vanishing line is best possible we also show how the differentials in this spectral sequence can be used to compute certain toda brackets

free transport for interpolated free group factors abstract in this article we study a form of free transport for the interpolated free group factors extending the work of guionnet and shlyakhtenko for the usual free group factors 11 our model for the interpolated free group factors comes from a canonical finite von neumann algebra m associated to a finite connected weighted graph v e 12 13 with this model we use an operator valued version of voiculescu s free difference quotient introduced in 13 to state a schwinger dyson equation which is valid for the generators of m we construct free transport for appropriate perturbations of this equation also m can be constructed using the machinery of shlyakhtenko s operator valued semicircular systems 24

pieri formulas for macdonald s spherical functions and polynomials we present explicit pieri formulas for macdonald s spherical functions or generalized hall littlewood polynomials associated with root systems and their q deformation the macdonald polynomials for the root systems of type a our pieri formulas recover the well known pieri formulas for the hall littlewood and macdonald symmetric functions due to morris and macdonald as special cases

discrete harmonic analysis on a weyl alcove abstract we introduce a representation of the double affine hecke algebra at the critical level q 1 in terms of difference reflection operators and use it to construct an explicit integrable discrete laplacian on the weyl alcove corresponding to an element in the center the laplacian in question is to be viewed as an integrable discretization of the conventional laplace operator on euclidean space perturbed by a delta potential supported on the reflection hyperplanes of the affine weyl group the bethe ansatz method is employed to show that our discrete laplacian and its commuting integrals are diagonalized by a finite dimensional basis of periodic macdonald spherical functions

singularly perturbed boundary value problems in discrete systems various types of singularly perturbed boundary value problems arising in discrete systems are formulated for the general type it is seen that the degenerate problem is of reduced order and hence shows its inability to accommodate all the given boundary conditions those left over boundary conditions are readmitted through appropriate corrections for the initial and final boundary layers a perturbation method is developed to obtain an approximate solution composed of an outer series initial boundary layer correction series and final boundary layer correction series an important feature of the method is that the corrections for the original boundary value problem are solved as an initial value problem and a final value problem facilitating a considerable reduction in computation an example is given to demonstrate the method

the analogues of entropy and of fisher s information measure in free probability theory i analogues of the entropy and fisher information measure for random variables in the context of free probability theory are introduced monotonicity properties and an analogue of the cramer rao inequality are proved

irreducible representations of free products of matrix algebras abstract in this paper we give a characterization of irreducible representation of i 1 m m n i c into m k n c where k n and the least common multiple n of n 1 n m is finite we also give a necessary condition for the existence of irreducible representation of i 1 m m n i c into m k n c

factoriality type classification and fullness for free product von neumann algebras abstract we give a complete answer to the questions of factoriality type classification and fullness for arbitrary free product von neumann algebras

state decomposition for singular perturbation order reduction a modal approach singular perturbation techniques for order reduction are based on decomposing the high order system into two parts approximation of the high order system dynamics by the low order model is mainly dependent on this partition this paper introduces a measure for the degree of dependence of the state variables on the high order dominant eigenvalues by means of this measure it is not only possible to find an appropriate decomposition yielding a good low order model but also to get an indication of the order of the reduced model two illustrative examples demonstrate the main results

universal toda brackets of ring spectra we construct and examine the universal toda bracket of a highly structured ring spectrum r this invariant of r is a cohomology class in the mac lane cohomology of the graded ring of homotopy groups of r which carries information about r and the category of r module spectra it determines for example all triple toda brackets of r and the first obstruction to realizing a module over the homotopy groups of r by an r module spectrum for periodic ring spectra we study the corresponding theory of higher universal toda brackets the real and complex k theory spectra serve as our main examples

infinite time regulators for singularly perturbed difference equations linear quadratic regulators for singularly perturbed difference equations are considered asymptotic behaviour of the optimal solution as the perturbation parameter tends to zero is studied the composite feedback control strategy of continuous time singularly perturbed systems is extended to the new problem

values of the pukanszky invariant in free group factors and the hyperfinite factor let a m b l2 m be a maximal abelian self adjoint subalgebra masa in a type ii1 factor m in its standard representation the abelian von neumann algebra a generated by a and jaj has a type i commutant which contains the projection ea a onto l2 a then a 1 ea decomposes into a direct sum of type in algebras for n 1 2 and those n s which occur in the direct sum form a set called the pukanszky invariant puk a also denoted pukm a when the containing factor is ambiguous in this paper we show that this invariant can take on the values s when m is both a free group factor and the hyperfinite factor and where s is an arbitrary subset of n the only previously known values for masas in free group factors were and 1 and some values of the form s are new also for the hyperfinite factor we also consider a more refined invariant that we will call the measure multiplicity invariant which was considered recently by neshveyev and stormer and has been known to experts for a long time we use the measure multiplicity invariant to distinguish two masas in a free group factor both having pukanszky invariant n for arbitrary n n

operations on resolutions and the reverse adams spectral sequence we describe certain operations on resolutions in abelian categories and apply them to calculate part of a reverse adams spectral sequence going from homotopy to homology for the space k z 2 n this calculation is then used to deduce that there is no space whose homotopy groups are the reduction mod 2 of 7l sr as another application of the operations we give a short proof of t y lin s theorem on the infinite projective dimension of all nonfree a modules

the krull filtration of the category of unstable modules over the steenrod algebra in the early 1990 s lionel schwartz gave a lovely characterization of the krull filtration of mathcal u the category of unstable modules over the mod p steenrod algebra soon after this filtration was used by the author as an organizational tool in posing and studying some topological nonrealization conjectures in recent years the krull filtration of mathcal u has been similarly used by castellana crespo and scherer in their study of h spaces with finiteness conditions recently gaudens and schwartz have given a proof of some of my conjectures in light of these topological applications it seems timely to better expose the algebraic properties of the krull filtration

hyperbolic configurations of roots and hecke algebras abstract this paper deals with infinite coxeter groups we use geometric techniques to prove two main results one is of lie theoretic nature it shows the existence of many hyperbolic configurations of three pairwise disjoint roots in a given coxeter complex provided it is not an euclidean tiling the other is both of algebraic and measure theoretic nature since it deals with hecke algebras it shows that for automorphism groups of buildings convolution algebras of bi invariant functions are never commutative provided the building is not euclidean proofs are of geometric nature the main idea is to exhibit and use enough trees of valency 3 inside a non affine coxeter complex

on structural decomposition and stabilization of large scale control systems graph theoretic concepts are used to decompose a large control system into a block triangular interconnection of input reachable subsystems stabilization of the system is thereby reduced to stabilization of a number of smaller subsystems the special structural properties of the obtained subsystems can be exploited to further simplify the stabilization problem

a method of order reduction for structural dynamics based on riccati iteration this paper presents a new method of order reduction based on recent work of a similar nature applicable to system dynamics and control this method provides a computational procedure for producing a condensed model which exactly preserves the slowest nl modes of the total n modes of the original model for almost any set of nt degrees of freedom retained in the condensed model the method can also be used to compute the eigensolutions corresponding to the n slowest modes of the original structural dynamics problem the accuracy of the condensed model and the speed accuracy performance of the eigensolver are compared with standard methods for a 90 degree of freedom cantilevered plate

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

spherical hecke algebras for kac moody groups over local fields we define the spherical hecke algebra h for an almost split kac moody group g over a local non archimedean field we use the hovel i associated to this situation which is the analogue of the bruhat tits building for a reductive group the stabilizer k of a special point on the standard apartment plays the role of a maximal open compact subgroup we can define h as the algebra of k bi invariant functions on g with almost finite support as two points in the hovel are not always in a same apartment this support has to be in some large subsemigroup g of g we prove that the structure constants of h are polynomials in the cardinality of the residue field with integer coefficients depending on the geometry of the standard apartment we also prove the satake isomorphism between h and the algebra of weyl invariant elements in some completion of a laurent polynomial algebra in particular h is always commutative actually our results apply to abstract locally finite hovels so that we can define the spherical algebra with unequal parameters

primitives and central detection numbers in group cohomology abstract fix a prime p given a finite group g let h g denote its mod p cohomology in the early 1990s henn lannes and schwartz introduced two invariants d 0 g and d 1 g of h g viewed as a module over the mod p steenrod algebra they showed that in a precise sense h g is respectively detected and determined by h d c g v for d d 0 g and d d 1 g with v running through the elementary abelian p subgroups of g the main goal of this paper is to study how to calculate these invariants we find that a critical role is played by the image of the restriction of h g to h c where c is the maximal central elementary abelian p subgroup of g a measure of this is the top degree e g of the finite dimensional hopf algebra h c h g f p a number that tends to be quite easy to calculate our results are complete when g has a p sylow subgroup p in which every element of order p is central using the benson carlson duality we show that in this case d 0 g d 0 p e p and a similar exact formula holds for d 1 as a bonus we learn that h e g p contains nontrivial essential cohomology reproving and sharpening a theorem of adem and karagueuzian in general we are able to show that d 0 g max e c g v v g if certain cases of benson s regularity conjecture hold in particular this inequality holds for all groups such that the difference between the p rank of g and the depth of h g is at most 2 when we look at examples with p 2 we learn that d 0 g 14 for all groups with 2 sylow subgroup of order up to 64 with equality realized when g su 3 4 en route we study two objects of independent interest if c is any central elementary abelian p subgroup of g then h g is an h c comodule and we prove that the subalgebra of h c primitives is always noetherian of krull dimension equal to the p rank of g minus the p rank of c if the depth of h g equals the rank of z g we show that the depth essential cohomology of g is nonzero reproving and extending a theorem of green and cohen macauley in a certain sense and prove related structural results