projections onto translation invariant subspaces of l1 g abstract let g be a locally compact abelian group a translation invariant subspace in l 1 g may or may not be complemented depending on the structure of its hull in techniques for deciding this complementation problem in a variety of situations are developed and illustrated with examples a complete characterization is obtained for those ideals with a discrete hull

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

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

additive models of probabilistic processes we propose a new model of probabilistic processes in this model a probability is assigned to the action of a prefix and a probability distribution is assigned to the components of a parallel composition in addition the probability of a transition of a probabilistic summation is evaluated as the sum of the probabilities of the same transition of summands multiplied by the probabilities associated to them in the summation the concepts of strong bisimulation degree and weak bisimulation degree are introduced these notions provide us with continuous spectra of strong bisimilarities weak bisimilarities and observation congruences which equate probabilistic processes with different degrees of belief various equational laws of probabilistic processes with respect to these equivalence relations are presented and substitutivities of these equivalence relations under various combinators are established

on stable orthogonal decompositions of idempotents in fact the two relative projectivities of a pointed group are equivalentin some sense and it is the same for the two relative freeness see 2 2 and2 29 below it is clear that the relative freeness implies the relative projectivity theconverse is certainly false to some extent our aim is just to look for theconditions which make the converse true if

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

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

a theory of communicating processes with value passing a semantic theory of process algebras which allows processes to communicate values is described a behavioural theory of testing is given for such processes and is modelled by an extension of acceptance trees a proof system is also given for this model and is shown to be both sound and complete finally the model is shown to be fully abstract with respect to the behavioural theory

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

2 blocks and 2 modular characters of the chevalley groups we first determine the distribution of the ordinary irreducible characters of the exceptional chevalley group g2 q q odd into 2 blocks this is done by using the method of central characters then all but two of the irreducible 2 modular characters are determined the results are given in the form of decomposition matrices the methods here involve concepts from modular representation theory and symbolic computations with the computer algebra system maple as a corollary the smallest degree of a faithful representation of g2 q q odd over a field of characteristic 2 is obtained

perfect isometries for principal blocks with abelian defect groups and elementary abelian 2 inertial quotients abstract letbbe the principalp block of a finite groupgwith an abelian defect grouppandea root ofbincg p if the inertial quotiente ng p e p cg p is an elementary abelian 2 group respectively a dihedral group of order 8 andp 3 thenband its brauer correspondent considered as blocks ofgandng p are isotypic and in particular there is a perfect isometry between them

on group stable commutative separable semisimple subalgebras in a g algebra a of a p group g over a perfect ground field there is a commutative separable semisimple g subalgebra such that any traces on relative projectivity in a can be controlled in the subalgebra and in a residually central sense the maximal such subalgebras form exactly one a g conjugacy class applying to modules the induced module of an indecomposable module of a subnormal subgroup of p primary index is characterized

fully group graded algebras and a theorem of fong abstract it is proved that any algebra fully graded by a finite group over a complete discrete valuation ring with an algebraically closed residue field of characteristic a prime p is morita equivalent to an embedded graded subalgebra which is a crossed product and an explicit way to get a decomposition of unity with a bounded length is shown when the finite group is p solvable a theorem of fong s type for fully graded algebras is obtained

defects of irreducible characters ofp soluble groups abstract we prove a refinement of the p soluble case of robinson s conjectural local characterization of the defect of an irreducible character

probabilistic bisimulations for quantum processes modeling and reasoning about concurrent quantum systems is very important for both distributed quantum computing and quantum protocol verification as a consequence a general framework formally describing communication and concurrency in complex quantum systems is necessary for this purpose we propose a model named qccs it is a natural quantum extension of classical value passing ccs which can deal with input and output of quantum states and unitary transformations and measurements on quantum systems the operational semantics of qccs is given in terms of probabilistic labeled transition system this semantics has many different features compared with the proposals in the available literature in order to describe the input and output of quantum systems which are possibly correlated with other components based on this operational semantics the notions of strong probabilistic bisimulation and weak probabilistic bisimulation between quantum processes are introduced furthermore some properties of these two probabilistic bisimulations such as congruence under various combinators are examined

on the hilbert schmidt semi norms ofl 1 of a nilpotent lie group in 2 appears the convolution product o f f with f on the non abelian group g combined with the abelian fourier transform on r a consequence of this mixture of non abelian with abelian operations is the fact that the integrand f f o exp need not be nonnegative this prohibits the extension of 2 to general ll functions it makes it also difficult to give estimations of ih f la s in terms o f i 7 it would be much better if one could replace 2 by

the indecomposability of a certain bimodule given by the brauer construction broue s abelian defect conjecture 3 6 2 predicts for a p block of a finite group g with an abelian defect group p a derived equivalence between the block algebra and its brauer correspondent by a result of rickard 11 such a derived equivalence would in particular imply a stable equivalence induced by tensoring with a suitable bimodule and it appears that these stable equivalences in turn tend to be obtained by gluing together morita equivalences at the local levels of the considered blocks see e g 4 6 3 8 3 1 12 4 1 and 13 5 6 a 4 1 this note provides a technical indecomposability result which is intended to verify in suitable circumstances the hypotheses that are necessary to apply gluing results as mentioned above this is used in 7 to show that broue s abelian defect group conjecture holds for nonprincipal blocks of the simple held group and the sporadic suzuki group

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

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

projections onto translation invariant subspaces of recently i klemes has characterized the complemented translation invariant subspaces of hl t in this paper we investigate the case of r the main results are that the hull of a complemented translation invariant sub space is e separated for some e 0 and that an e separated subset of r which is in the ring generated by cosets of closed subgroups of r intersected with r and lacunary sequences is the hull of a complemented ideal

g algebras jacobson radical and almost split sequences keywords finite group indecomposable kg module sas sequence almost split exact sequences restriction relative jacobson radicals local criterion multiplicity module vertex source indecomposable projective module twisted group algebra induction reference ctg article 1988 006doi 10 1007 bf01393690 record created on 2008 12 16 modified on 2017 05 12

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