on centers of blocks with one simple module abstract let g be a finite group and let b be a non nilpotent block of g with respect to an algebraically closed field of characteristic 2 suppose that b has an elementary abelian defect group of order 16 and only one simple module the main result of this paper describes the algebra structure of the center of b this is motivated by a similar analysis of a certain 3 block of defect 2 in kessar 2012 15

multiple positive solutions of conjugate boundary value problems with singularities the existence of one or several positive solutions for some nth order differential equations with conjugate boundary conditions is obtained the approach is to employ the well known results on the existence of positive solutions for hammerstein integral equations obtained recently by the author this avoids utilizing the theory of fixed point index for compact maps defined on cones directly new properties on the kernels corresponding to the boundary value problems are provided and then employed to prove new properties of nonzero positive solutions for these boundary value problems and new inequalities on functions satisfying the conjugate boundary conditions our results improve and generalize many recent results

the structure of time optimal trajectories for single input systems in the plane the c nonsingular case for single input c infty systems in the plane in which the control enters linearly we prove if the system is suitably nondegenerate that the time optimal trajectories are finite concatenations of bang bang and singular arcs with local bounds on the number of switchings

broue s abelian defect group conjecture holds for the harada norton sporadic simple group hn abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent rickard equivalent this conjecture is called broue s abelian defect group conjecture we prove in this paper that broue s abelian defect group conjecture is true for a non principal 3 block a with an elementary abelian defect group p of order 9 of the harada norton simple group hn it then turns out that broue s abelian defect group conjecture holds for all primes p and for all p blocks of the harada norton simple group hn

generalized baire category and differential inclusions in banach spaces soit e un espace de banach separable reflexif et on considere le probleme de cauchy x t f x t x 0 x 0 e ou f est une fonction multiforme continue de hausdorff a valeurs bornees fermees on demontre l existence locale d une solution en supposant que la fermeture convexe de f x 0 a une codimension finie

blocks with frobenius inertial quotients abstract in the paper we prove that a perfect isometry between a block of a finite group and its brauer correspondent can be extended to a perfect isometry between a block of a larger finite group and its brauer correspondent with suitable hypotheses we also obtain a similar result for derived equivalences

universal deformation rings and tame blocks let k be an algebraically closed field of positive characteristic and let g be a finite group suppose b is a block of kg of infinite tame representation type we find all finitely generated kg modules v that belong to b and whose endomorphism ring is isomorphic to k and determine the universal deformation ring r g v for each of these modules

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

a local property of basic rickard equivalences abstract let p be a prime and k be an algebraically closed field of characteristic p let g and g be two finite groups b and b be blocks of g and g and p e and p e be maximal brauer b g and b g pairs if kgb and k g b are basic rickard equivalent then there is a group isomorphism p p such that it induces an equivalence between the brauer categories of kgb and k g b and that for any brauer b g pair q f contained in p e and any subgroup k of the image of n g q f in aut q the block algebras k n g k q f and k n g k q f are basic rickard equivalent where q q f is the block of k c g q such that q f p e and k denotes the image of k in aut q

positive solutions for a system of nonlinear hammerstein integral equations and applications abstract we are concerned with the existence and multiplicity of positive solutions for the system of nonlinear hammerstein integral equations u t a b k 1 t s g 1 s f 1 s u s v s d s v t a b k 2 t s g 2 s f 2 s u s v s d s where k i c a b a b r f i c a b r 2 r and g i c a b is almost everywhere positive on a b i 1 2 we overcome the difficulty arising from the difference between the two kernels k 1 t s g 1 s and k 2 t s g 2 s by defining certain integral constants and use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing jensen s inequality for concave functions and nonnegative matrices our nonlinearities f and g cover the following three cases the first with both superlinear the second with both sublinear and the last with one sublinear and the other superlinear our main results are applied to establish the existence and multiplicity of positive symmetric solutions for an elliptic system in an annulus

equivalences between blocks of p local mackey algebras let g be a finite group and k o k be a p modular system let r o or k there is a bijection between the blocks of the group algebra and the blocks of the so called p local mackey algebra mu 1 r g let b be a block of rg with abelian defect group d let b be its brauer correspondant in n g d it is conjectured by broue that the blocks rgb and rng d b are derived equivalent here we look at equivalences between the corresponding blocks of p local mackey algebras we prove that an analogue of the broue s conjecture is true for the p local mackey algebras in the following cases for the principal blocks of p nilpotent groups and for blocks with defect 1

on picard groups of blocks of finite groups we show that the subgroup of the picard group of ap block ofa finite group given by bimodules with endopermutation sources modulo theautomorphism group of a source algebra is determined locally in terms of thefusion system on a defect group we show that the picard group of a block overa complete discrete valuation ringoof characteristic zero with an algebraicclosurekoffpas residue field is a colimit of finite picard groups of blocks overp adic subrings ofo we apply the results to blocks with an abelian defectgroup and frobenius inertial quotient and specialise this further to blockswith cyclic or klein four defect groups

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

broueʼs abelian defect group conjecture holds for the double cover of the higman sims sporadic simple group abstract in the representation theory of finite groups there is a well known and important conjecture due to broue saying that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent we prove in this paper that broue s abelian defect group conjecture and even rickard s splendid equivalence conjecture are true for the faithful 3 block a with an elementary abelian defect group p of order 9 of the double cover 2 hs of the higman sims sporadic simple group it then turns out that both conjectures hold for all primes p and for all p blocks of 2 hs

equivariant splendid rickard equivalences abstract broue s conjecture says that if a finite group h has an abelian sylow p subgroup p then the principal blocks of h and n h p are splendidly rickard equivalent in this paper broue s conjecture is reduced to simple groups with a stability condition a structure theorem on finite groups with abelian sylow p subgroups due to kimmerle and sandling is used

the most likely path of a differential inclusion can be used in alternative to stochastic processes as a model for systems whose evolution is non deterministic compared with the rich mathemati cal theory which is currently available for random processes however dif ferential inclusions have remained a rather thin subject concerned mainly with the existence of solutions and with the topological properties of the set of trajectories the present paper is an attempt to widen the scope of this theory introducing the notion of likelihood for a solution of a differential inclusion and formulating a corresponding class of estimation prediction and filtering problems to do this a simple approach first comes to mind define some probabil ity measure on the set of trajectories of 1 1 and formulate the prediction and filtering problems accordingly unfortunately there seems to be no canonical probability distribution which is supported precisely on the solution set of 1 1 the choice of any particular distribution would thus require considerable additional information about the system to be modeled for this reason we consider a new definition of likelihood which is entirely independent of probability theory relying solely on the metric structure if 9 denotes the family of all solutions of 1 1 and u e 9 a rough estimate of how many trajectories u e b remain close to u is given by fl d u f iv t u t l 0 as e 0 the i mum of the quantities 1 2 is a well defined number 155

on a nonlinear hammerstein integral equation with a parameter abstract this paper following theories for asymptotically linear operators the schaefer fixed point theorem decomposition of operators and critical point theory is mainly concerned with the existence and multiplicity of solutions to a nonlinear hammerstein integral equation with a parameter the results show that when the nonlinearity satisfies certain conditions different parametric intervals lead to different existence results however in some cases only the sign of the parameter makes a contribution to the existence of solutions for the problem our results can be applied to some well known boundary value problems and some examples are given

extensions of rickard equivalences broue conjectures that a block of a finite group g with abelian defect group p is rickard equivalent to its brauer correspondent in the normalizer ng p we find a character theoretic criterion on extensions of rickard equivalences between blocks as an application we prove that the conjecture holds for the principal block of a finite group with abelian defect group and cyclic hyperfocal subgroup

blocks with defect group z2n z2n z2m abstract in this paper we prove that a block algebra with defect group z 2 n z 2 n z 2 m where n 2 and m is arbitrary is morita equivalent to its brauer correspondent

broueʼs abelian defect group conjecture holds for the sporadic simple conway group co3 in the representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block an of the normaliser ng p of p in g are derived equivalent rickard equivalent this conjecture is called strong version of broue s abelian defect group conjecture in this paper we prove that the strong version of broue s abelian defect group conjecture is true for the non principal 2 block a with an elementary abelian defect group p of order 8 of the sporadic simple conway group co3 this result completes the verification of the strong version of broue s abelian defect group conjecture for all primes p and for all p blocks of co3

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

trivial source bimodule rings for blocks and p permutation equivalences we associate with any p block of a finite group a grothendieck ring of certain p permutation bimodules we extend the notion of p permutation equivalences introduced by boltje and xu 4 to source algebras of p blocks of finite groups we show that a p permutation equivalence between two source algebras a b of blocks with a common defect group and same local structure induces an isotypy

multiple positive eigenfunctions of singular hammerstein integral equations with applications to boundary value problems abstract new results on eigenvalue intervals and the existence of one or several positive eigenfunctions for singular hammerstein integral equations are obtained via the fixed point index for compact maps applications of these results will be given to two point three point and periodic boundary value problems

the extended brauer quotient of n interior g algebras abstract in this note we generalize the extended brauer quotient defined by l puig and y zhou in 4 section 3 to the case of n interior g algebras where n is a normal subgroup of a finite group g we use this extended brauer quotient on permutation algebras to establish some correspondences that generalize known results that hold in the group algebra case

relaxation theorem for the evolution differential inclusions abstract in this paper we use an improved version of baire category method to prove the existence of solutions to the evolution differential inclusion ax ext f t x under the hausdorff noncompactness measure condition we also obtain a density result for the evolution differential inclusion

trivial source modules in blocks with cyclic defect groups we shall present a method to get trivial source modules easily just by looking at values of ordinary characters at non identity p elements in finite groups instead of doing huge calculation the method is only for a case where defect groups are cyclic nevertheless it works well at least when we want to prove broue s abelian defect group conjecture for blocks which have elementary abelian defect groups of order p2

on morita and derived equivalences for cohomological mackey algebras by results of the second author a source algebra equivalence between two p blocks of finite groups induces an equivalence between the categories of cohomological mackey functors associated with these blocks and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological mackey functors the main result of this paper proves a partial converse an equivalence resp rickard equivalence between the categories of cohomological mackey functors of two blocks of finite groups induces a permeable morita resp derived equivalence between the two block algebras

a baire category approach to the bang bang property abstract the aim of this paper is to develop a new technique based on the baire category theorem in order to establish the closedness of reachable sets and the existence of optimal trajectories for control systems without the usual convexity assumptions the bang bang property is proved for a new class of concave multifunctions characterized by the existence of suitable linear selections the proofs rely on lyapunov s theorem in connection with a baire category argument

multiple eigenvalues for singular hammerstein integral equations with applications to boundary value problems new results on the existence of multiple positive eigenvalues for singular hammerstein integral equations are obtained the radius of the spectrum of a linear hammerstein integral operator is first employed to obtain a better upper bound for the eigenvalues we seek these results are applied to treat some second order ordinary differential equations with two point three point and some periodic boundary value problems

group graded basic morita equivalences abstract we introduce group graded basic morita equivalences between algebras determined by blocks of normal subgroups and by using the extended brauer quotient we show that they induce graded basic morita equivalences at local levels

affirmative answer to a question of feit as he points out if p is abelian the affirmative answer follows from dade s classification 4 our purpose here is to show that the general case reduces to the abelian one which answers affirmatively feit s question more generally in 4 dade determines the cap group associated with a finite abelian p group showing in particular that this group is finitely generated our main result here cf theorem 2 2 below implies that finite generation is still true in the non abelian case cf corollary 2 4 below this result and the main steps of a proof were already announced in 17 section81 and here we are just discharging ourselves of an old debt actually as we said in 7 section81 our result would follow from a complete classification of endo permutation modules

existence of multiple solutions for some nonlinear boundary value problems abstract by imposing one sided conditions on the nonlinearity where neither regularity nor uniformity is required we prove the existence of either a nonnegative or a nonpositive solution for first and second order ordinary differential equations with periodic neumann or dirichlet boundary conditions positone and nonpositone problems are considered some nonexistence results are also obtained when using generalized ambrosetti prodi type conditions we get the existence of nonnegative and nonpositive solutions for first and second order periodic or neumann boundary value problems our method of proof makes use of topological degree arguments in cones

multiple positive solutions of hammerstein integral equations and applications to periodic boundary value problems new results on the existence of multiple positive solutions of a hammerstein integral equation of the formz t email protected gk t s f s z s ds az t are obtained where f may have singularities in its first or second variable these results generalize some previous results obtained by the author applications of these results are given to the existence of multiple positive solutions for singular first or second order differential equations with periodic boundary conditions these results are often new and some of them improve many known results

duality in g algebras keywords finite group complete discrete valuation ring symmetric g algebra symmetric bilinear form projective ideal symmetric algebra rg lattice unimodular symmetric g algebra almost projective ideal almost split sequences block defect groups virtually irreducible lattices splitting trace lattices reference ctg article 1988 005doi 10 1007 bf01161746 record created on 2008 12 16 modified on 2017 05 12

hyperfocal subalgebras of blocks and computation of characters abstract in terms of puig s theory on blocks it is described how to compute the irreducible characters of any block from the hyperfocal subalgebra of the block and the source algebra and the characters of a block whose hyperfocal subgroup is a direct factor of its defect group are characterized

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

basic morita equivalences and isotypies abstract basic morita equivalences and isotypies between blocks are due to l puig and m broue respectively in this paper we prove that a basic morita equivalence between blocks induces an isotypy if and only if the value at an element u of the character of a source of the bimodule inducing the basic morita equivalence is m u where m u is the multiplicity of the indecomposable direct summand unique up to isomorphism with vertex u of the restriction to u of the source

derived equivalent tame blocks abstract in this article we provide derived equivalences between several blocks of tame representation type based on erdmann s work on morita equivalence classes of tame blocks we obtain a classification of tame blocks up to derived equivalence as in erdmann s work in the case of two simple modules our classification is only complete up to scalars occurring in certain relations

the broue conjecture for the faithful 3 blocks of 4 m22 abstract we verify broue s conjecture for the faithful 3 blocks of defect 2 of the non split central extension of the sporadic simple mathieu group m 22 by a cyclic group of order 4 the proof is based on a strategy due to okuyama and rickard where a stable equivalence is lifted to a derived equivalence the stable equivalence in turn is provided by exploiting a result due to puig to handle this particular example next to theoretical investigations we apply a whole bunch of computational tools

on the characters of nilpotent blocks over small ground fields abstract i characterize how the irreducible characters of a nilpotent block over a small ground field are determined one by one by the irreducible characters of its defect groups

on some saturated triples and hyperfocal subgroups abstract let b denote a primitive idempotent of the subalgebra k h g in kh of g stable elements where h is a normal subgroup of a finite group g which acts by conjugation on h and k is an algebraically closed field of characteristic p using a generalization of block induction to the case of primitive idempotents in algebras of the form k h g we show that when the hyperfocal subgroup is abelian the fusion system associated to b respectively to the induced stable primitive idempotent of the generalized brauer pair corresponding to the hyperfocal subgroup are the same

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

remarks on the extended brauer quotient abstract we study the properties of the extended brauer quotient introduced by puig and zhou in the case of a group graded algebra we also introduce an alternative construction of the quotient

source algebras and source modules the aim of this article is to give a self contained approach in module theoretic terms to two fundamental results in block theory due to puig 6 14 6 first there is an embedding of the source algebra of the brauer correspondent of a block of some finite group into a source algebra of that block and second the source algebras of the brauer correspondence can be described explicitly our proof of the first result theorem 5 and its corollary 6 below is essentially the translation to our terminology of the proof in 1 4 10 the second result describing the source algebras of the brauer correspondent follows also from 3 but the proofs in 3 use both the main result on the structure of nilpotent blocks in 5 as well as techniques from 6 sects 4 6 while our approach from proposition 9 onwards requires only some classical results on the structure of blocks with a central defect group an account of the results in 6 on source algebras of blocks with a normal defect group can also be found in 7 sect 45 except for the explicit description of the central extension e see section 10 below as being defined in terms of the multiplicity algebra of the block which is quoted in 7 45 10 b without proof referring back to 6 at the end of 7 sect 45

rationality of eigenvalues of cartan matrices in finite groups abstract we study the case in which eigenvalues and elementary divisors of a cartan matrix of a p block b of a finite group coincide in several cases we prove the coincidence occurs if and only if the perron frobenius eigenvalue of the cartan matrix is equal to the order of a defect group of b

extremal solutions of differential inclusions via baire category a dual approach abstract let f be a continuous multifunction on r n with compact convex values for any vector w let f w x f x be the subset of points which maximize the inner product with w call w the set of all continuous functions w 0 t r n with the following property all solutions to the cauchy problem x t f w t x t x 0 0 are also solutions to x t ext f x t we prove that w is residual in c 0 t r n

baire category and boundary value problems for ordinary and partial differential inclusions under caratheodory assumptions by using the baire category method we prove an existence result for boundary value problem of dirichlet type for non convex ordinary differential inclusions under caratheodory assumptions by counterexamples we show that an analogous existence result is non valid for non convex partial differential inclusions

the parametrization of interior algebras keywords finite group indecomposable og lattice invariants vertex source multiplicity module indecomposable projective lattice twisted group algebra primitive interior g algebras reference epfl article 130446doi 10 1007 bf02571667 record created on 2008 12 16 modified on 2017 05 12

on the rational second kind chebyshev pseudospectral method for the solution of the thomas fermi equation over an infinite interval in this paper we propose a pseudospectral method for solving the thomas fermi equation which is a nonlinear singular ordinary differential equation on a semi infinite interval this approach is based on the rational second kind chebyshev pseudospectral method that is indeed a combination of tau and collocation methods this method reduces the solution of this problem to the solution of a system of algebraic equations the slope at origin is provided with high accuracy comparison with some numerical solutions shows that the present solution is effective and highly accurate