formal group theoretic generalizations of the necklace algebra including aq deformation abstract n metropolis and g c rota adv math 50 1983 95 125 studied thenecklace polynomials and were lead to define thenecklace algebraas a combinatorial model for the classical ring ofwitt vectors which corresponds to the multiplicative formal group lawx y xy in this paper we define and study a generalized necklace algebra which is associated with an arbitrary formal group lawfover a torsion free ringa the map from the ring of witt vectors associated withfto the necklace algebra is constructed in terms of certain generalizations of the necklace polynomials we present a combinatorial interpretation for these polynomials in terms of words on a given alphabet the actions of theverschiebungandfrobeniusoperators as well as of thep typification idempotentare described and interpreted combinatorially aq analogue and other generalizations of thecyclotomic identityare also presented in general the necklace algebra can only be defined over the rationalizationa q nevertheless we show that for the family of formal group laws over the integersfq x y x y qxy q z we can define the corresponding necklace algebras over z we classify these algebras and define isomorphic ring structures on the groups of witt vectors and the groups of curves associated with the formal group lawsfq theq necklace polynomials which turn out to benumerical polynomialsin two variables can be interpreted combinatorially in terms of so calledq words and they satisfy an identity generalizing a classical one

diffusion in heterogeneous media diffusion processes in heterogeneous media and biological systems in particular are riddled with the difficult theoretical issue of whether the true origin of anomalous behavior is renewal or memory or a special combination of the two accounting for the possible mixture of renewal and memory sources of subdiffusion is challenging from a computational point of view as well this problem is exacerbated by the limited number of techniques available for solving fractional diffusion equations with time dependent coefficients we propose an iterative scheme for solving fractional differential equations with time dependent coefficients that is based on a parametric expansion in the fractional index we demonstrate how this method can be used to predict the long time behavior of nonautonomous fractional differential equations by studying the anomalous diffusion process arising from a mixture of renewal and memory sources

biset transformations of tambara functors abstract if we are given an h g biset u for finite groups g and h then any mackey functor on g can be transformed by u into a mackey functor on h in this article we show that the biset transformation is also applicable to tambara functors when u is right free and in fact forms a functor between the category of tambara functors on g and h this biset transformation functor is compatible with some algebraic operations on tambara functors such as ideal quotients or fractions in the latter part we also construct the left adjoint of the biset transformation

tambarization of a mackey functor and its application to the witt burnside construction abstract for an arbitrary group g a semi mackey functor is a pair of covariant and contravariant functors from the category of g sets and is regarded as a g bivariant analog of a commutative semi group in this view a g bivariant analog of a semi ring should be a semi tambara functor a tambara functor is firstly defined by tambara which he called a tnr functor when g is finite as shown by brun a tambara functor plays a natural role in the witt burnside construction it will be a natural question if there exist sufficiently many examples of tambara functors compared to the wide range of mackey functors in the first part of this article we give a general construction of a tambara functor from any mackey functor on an arbitrary group g in fact we construct a functor from the category of semi mackey functors to the category of tambara functors this functor gives a left adjoint to the forgetful functor and can be regarded as a g bivariant analog of the monoid ring functor in the latter part when g is finite we investigate relations with other mackey functorial constructions crossed burnside ring elliott s ring of g strings jacobson s f burnside ring all these lead to the study of the witt burnside construction

the spectrum of the burnside tambara functor on a finite cyclic p group abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this analogy previously we have defined an ideal of a tambara functor in this article we calculate the prime spectrum of the burnside tambara functor when g is a finite cyclic p group for a prime integer p

biorthogonal systems and quotient spaces via baire category methods we show that every banach space x of density smaller that the baire category number open image in new window admits a quotient with a long schauder basis that can be taken of length 1 if x is not separable so assuming that the baire category number open image in new window does not take its minimal possible value a banach space x is separable if and only if all biorthogonal systems of x are countable

separable quotients for less than barrelled function spaces abstract we solve the separable quotient problem for spaces c p x and c c x that are dual locally complete dlc greatly extending the positive solution for barrelled c c x indeed ours is either the best or next to best weak barrelledness extension possible yet some interesting non dlc spaces c p x and c c x also admit separable quotients

ideals of tambara functors abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this article we consider a g bivariant analog of the ideal theory for tambara functors

dynamic versus thermodynamic approach to non canonical equilibrium abstract we study the dynamic and thermodynamic origin of non canonical equilibria and we discuss their connection with the generalized central limit theorem and the micro canonical boltzmann principle we reach the conclusion that the zeroth law of thermodynamics and the boltzmann principle are fulfilled thanks to an apparent fault turned into a benefit the dynamic approach can only produce a truncated form of inverse power law equilibrium

congruence relations characterizing the representation ring of the symmetric group abstract using the theory of burnside rings various canonical families of congruence relations are exhibited which hold for characters of the symmetric group and characterize the ring generated by them as a subring of the ring of integer valued class functions as a corollary the irreducible characters are characterized as integer valued class functions n z which satisfy those congruence relations and the standard conditions 1 0 and n 2 n

crossed burnside rings and bouc s construction of green functors abstract we use a formula for primitive idempotents of the crossed burnside ring given by f oda and t yoshida and a result from the theory of green functors obtained by s bouc to prove an induction theorem for the drinfel d double for a finite group over the complex field we obtain artin s induction theorem for group algebras as a corollary of the theorem

an infinite ramsey theorem and some banach space dichotomies a problem of banach asks whether every infinite dimensional banach space which is isomorphic to all its infinite dimensional subspaces must be isomorphic to a separable hilbert space in this paper we prove a result of a ramsey theoretic nature which implies an interesting dichotomy for subspaces of banach spaces combined with a result of komorowski and tomczakjaegermann this gives a positive answer to banachxs problem we then generalize the ramsey theoretic result and deduce a further dichotomy for banach spaces with an unconditional basis

fluctuation dissipation process without a time scale we study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long range correlations we make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically with a good agreement between theory and numerical treatment as a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution the distribution tails are truncated the distribution border is signaled by sharp peaks and in the weak dissipation limit the central distribution body becomes identical to a truncated l evy distribution

witt vectors and the algebra of necklaces where u is the classical mobius function m a n is called a necklace polynomial we shall be concerned with some remarkable identities satisfied by the polynomials m a n which apparently have not been previously noticed specifically we prove that m a n can be expressed as a quadratic polynomial in m a i and mj that m a n can be expressed linearly and integrally in terms of m a i the proofs given below of these identities are entirely combinatorial theorems l 6

the witt vectors for green functors abstract we define twisted hochschild homology for green functors this construction is the algebraic analogue of the relative topological hochschild homology thh c n and under flatness conditions it describes the e 2 term of the kunneth spectral sequence for relative thh applied to ordinary rings we obtain new algebraic invariants extending hesselholt s construction of the witt vectors of noncommutative rings we interpret our construction as providing witt vectors for green functors

operators whose dual has non separable range let x and y be separable banach spaces and t x y be a bounded linear operator we characterize the non separability of t y by means of fixing properties of the operator t

a generalized cyclotomic identity abstract in this paper we prove a generalization of the cyclotomic identity for each group g satisfying suitable finiteness conditions we prove this generalized cyclotomic identity by counting coloured g set structures the cyclotomic identity corresponds to taking g the free abelian group of rank one for the free abelian group of rank two for example we get an analogous identity involving the generating function of the partition function interalia we show that studying g set structures gives a unified and conceptually simple approach to other classical combinatorial identities not to the author s knowledge previously linked in the literature

r analogue of the burnside ring of profinite groups and free lie algebras abstract let r be a finite dimensional torsion free special ring in this paper we generalize the results in dress and siebeneicher adv in math 70 1988 89 78 1989 1 by constructing r analogue r g of the burnside ring of profinite groups g in particular we remark that the grothendieck lie module denominator identity of free lie algebras in oh necklace rings and logarithmic functions preprint kias 2003 is closely related to the canonical isomorphism between r g and grothendieck s ring of formal power series with coefficients in r and constant term 1

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

crossed burnside rings i the fundamental theorem abstract let g be a finite group and s a finite g monoid a crossed g set over s is a finite g set equipped with a g map into s called a weight function a crossed burnside ring x g s is the grothendieck ring of the category of crossed g sets with respect to disjoint unions and tensor products in this paper we prove the fundamental theorem of crossed burnside rings and an idempotent formula at characteristic 0

categorical aspects of generating functions i exponential formulas and krull schmidt categories abstract in this paper we study formal power series with exponents in a category for example the generating function of a category e with finite hom sets is defined by e t tx aut x where the summation is taken over all isomorphism classes of objects of e we can use such power series to enumerate the number of e structures along a faithful functor theorem 4 6 our theory is closely related to the theory of species joyal 1981 a species can be identified with a faithful functor from a groupoid to the category of finite sets theorem 3 6 we use mainly the concept of faithful functors with finite fibers instead of species so that we can separate the roles categories and functors play for example the exponential formula e t exp con e t means the unique coproduct decomposition property theorem 5 8 in the final section we give some applications of our theory to rather classical enumerations

witt burnside ring and burnside ring over a special λ ring abstract given an arbitrary group g we construct a covariant functor f g from the category of special rings to that of commutative rings with unity when g is a strongly complete profinite group it will be used to reconstruct the functor n r g which was first introduced in y t oh r analogue of the burnside ring of profinite groups and free lie algebras adv math 190 2005 1 46 to investigate the structure of witt burnside rings over special rings more precisely given a special ring r we show that n r g r is functorially isomorphic to f g r j g r for some ideal j g r of f g r the connection to the functor f g due to j j graham generalized witt vectors adv math 99 1993 248 263 will also be demonstrated

q analog of the mobius function and the cyclotomic identity associated to a profinite group abstract let g be a profinite group and q an indeterminate in this paper we introduce and study a q analog of the mobius function and the cyclotomic identity arising from the lattice of open subgroups of g when q is any integer we show that they have close connections with the functors w g q nr g q and nr g q introduced in y t oh q deformation of witt burnside rings math z 257 2007 151 191 in particular we interpret the multiplicative property of the inverse of the table of marks and the mobius function of g as a composition property of certain functors classification of w g q nr g q and nr g q up to strict natural isomorphism as q varies over the set of integers and its application will be dealt with too

q deformation of witt burnside rings in this paper we construct a q deformation of the witt burnside ring of a profinite group over a commutative ring where q ranges over the set of integers when q 1 it coincides with the witt burnside ring introduced by dress and siebeneicher adv math 70 87 132 1988 to achieve our goal we first show that there exists a q deformation of the necklace ring of a profinite group over a commutative ring as in the classical case i e the case q 1 q deformed witt burnside rings and necklace rings always come equipped with inductions and restrictions we also study their properties as a byproduct we prove a conjecture due to lenart j algebra 199 703 732 1998 finally we classify mathbb w g q up to strict natural isomorphism in case where g is an abelian profinite group

on the andre quillen homology of tambara functors abstract we lift to equivariant algebra three closely related classical algebraic concepts abelian group objects in augmented commutative algebras derivations and kahler differentials we define mackey functor objects in the category of tambara functors augmented to a fixed tambara functor r and we show that the usual square zero extension gives an equivalence of categories between these mackey functor objects and ordinary modules over r we then describe the natural generalization to tambara functors of a derivation building on the intuition that a tambara functor has products twisted by arbitrary finite g sets and we connect this to square zero extensions in the expected way finally we show that there is an appropriate form of kahler differentials which satisfy the classical relation that derivations out of r are the same as maps out of the kahler differentials

the crossed burnside rings iii the dress construction for a tambara functor abstract we discuss the dress construction for a tambara functor associated to a finite commutative monoid with action of a finite group

a density version of the halpern lauchli theorem abstract we prove a density version of the halpern lauchli theorem this settles in the affirmative a conjecture of r laver specifically let us say that a tree t is homogeneous if t has a unique root and there exists an integer b 2 such that every t t has exactly b immediate successors we show that for every d 1 and every tuple t 1 t d of homogeneous trees if d is a subset of the level product of t 1 t d satisfying lim sup n d t 1 n t d n t 1 n t d n 0 then there exist strong subtrees s 1 s d of t 1 t d having a common level set such that the level product of s 1 s d is a subset of d

partial tambara structure on the burnside biset functor induced from a derivator like system of adjoint triplets abstract in the previous article a mackey functor theoretic interpretation of biset functors we have constructed the 2 category s of finite sets with variable finite group actions in which bicoproducts and bipullbacks exist as shown in it biset functors can be regarded as a special class of mackey functors on s in this article we equip s with a system of adjoint triplets which satisfies properties analogous to a derivator this system encodes the six operations for finite groups as a corollary we show that the associated burnside rings satisfy analogous properties to a tambara functor in the context of biset functor theory

nested witt vectors and their q deformation abstract let n n be a truncation set we study the ring of n nested witt vectors and its q deformation given two arbitrary integers q and r we provide a necessary and sufficient condition of a so that w n q a and w n r a should be strictly isomorphic to each other also an isomorphism of functors w n q w m q w m n q will be established for coprime truncation sets m and n as a byproduct we deal with interesting connections between nested witt vectors and other areas such as generalized mobius functions and numerical polynomials i e polynomials which take integral values at integer arguments

ramsey families of subtrees of the dyadic tree we show that for every rooted finitely branching pruned tree t of height w there exists a family f which consists of order isomorphic to t subtrees of the dyadic tree c 0 1 n with the following properties i the family f is a g subset of 2 c ii every perfect subtree of c contains a member of f iii if k is an analytic subset of f then for every perfect subtree s of c there exists a perfect subtree s of s such that the set a f a c s either is contained in or is disjoint from k

induction formulae for mackey functors with applications to representations of the twisted quantum double of a finite group abstract in the theory of canonical induction formulae for mackey functors boltje 4 demonstrated that the plus constructions together with the mark morphism are useful for the study of canonical versions of induction theorems analogous to those in representation theory of finite groups in this paper we present a short exact sequence for the plus constructions derived from cauchy frobenius lemma and apply it to the proof of boltje s integrality result for canonical induction formulae the methods appearing in boltje s theory combined with the dress construction for mackey functors are applicable to induction theorems on representations of the twisted quantum double of a finite group as a sequel to such a research we describe canonical versions of two induction theorems whose origins are artin s induction theorem and brauer s induction theorem on c characters of a finite group

crossed burnside rings ii the dress construction of a green functor abstract we present some results about the dress construction of green functor associated to a g monoid in particular we see that the crossed burnside rings the representation rings of quantum double and hochschild cohomology rings are constructed by the dress construction of some green functors

higher topological cyclic homology and the segal conjecture for tori abstract we investigate higher topological cyclic homology as an approach to studying chromatic phenomena in homotopy theory higher topological cyclic homology is constructed from the fixed points of a version of topological hochschild homology based on the n dimensional torus and we propose it as a computationally tractable cousin of n fold iterated algebraic k theory the fixed points of toral topological hochschild homology are related to one another by restriction and frobenius operators we introduce two additional families of operators on fixed points the verschiebung indexed on self isogenies of the n torus and the differentials indexed on n vectors we give a detailed analysis of the relations among the restriction frobenius verschiebung and differentials producing a higher analog of the structure hesselholt and madsen described for 1 dimensional topological cyclic homology we calculate two important pieces of higher topological cyclic homology namely topological restriction homology and topological frobenius homology for the sphere spectrum the latter computation allows us to establish the segal conjecture for the torus which is to say to completely compute the cohomotopy type of the classifying space of the torus

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

decomposition of the witt burnside ring and burnside ring of an abelian profinite group abstract let g h be abelian profinite groups whose orders are coprime and assume that q ranges over the set of integers the aim of this paper is to establish an isomorphism of functors w g q w h q w g h q where w g q denotes the q deformed witt burnside ring functor of g introduced in y t oh q deformation of witt burnside rings math z 207 1 2007 151 191 to do this we first establish an isomorphism of functors b g q b h q b g h q where b g q denotes the q deformed burnside ring functor of g which was also introduced in y t oh q deformation of witt burnside rings math z 207 1 2007 151 191 as an application we derive a pseudo multiplicative property of the q mobius function associated to the lattice of open subgroups of the direct sum of g and h

generalized burnside rings and group cohomology we define the cohomological burnside ring b n g m of a finite group g with coefficients in a zgmodule m as the grothendieck ring of the isomorphism classes of pairs x u where x is a g set and u is a cohomology class in a cohomology group h n x g m the cohomology groups h x g m are defined in such a way that h x g m i h hi m when x is the disjoint union of transitive g sets g hi i fa is an abelian group with trivial action then b 1 g a is the same as the monomial burnside ring over a and when m is taken as a g monoid then b 0 g m is equal to the crossed burnside ring b c g m we discuss the generalizations of the ghost ring and the mark homomorphism and prove the fundamental theorem for cohomological burnside rings we also give an interpretation of b 2 g m in terms of twisted

witt vectors and tambara functors abstract we give a combinatorial description of the ring of g witt vectors on a polynomial algebra over the integers for every finite group g using this description we show that the functor which takes a commutative ring with trivial action of g to its ring of witt vectors coincides with the left adjoint of the algebraic functor from the category of g tambara functors to the category of commutative rings with an action of g

composition factors from the table of marks let b g be the burnside ring for a finite group g and let t g be the table of marks of g it is known that in general neither b g nor t g determines the finite group g that is one can easily construct pairs of non isomorphic finite groups such that their table of marks is the same hence their burnside rings are isomorphic in this note we show that the composition factors of g are determined by the table of marks t g

unconditional basic sequences in spaces of large density abstract we study the problem of the existence of unconditional basic sequences in banach spaces of high density we show in particular the relative consistency of the statement that every banach space of density contains an unconditional basic sequence

generalized witt vectors abstract the witt burnside ring as contrived by a dress and c siebeneicher adv in math 70 1988 87 132 is a generalisation of the ring of witt vectors in this paper we characterise this ring algorithmically generalising the carryless witt vectors described by n metropolis and g c rota adv in math 50 1983 95 125 this approach has the merit of simplifying dress main theorem which asserts the existence of this ring and a few properties that characterise it it also makes the definition of rota s carryless witt vectors more natural

q deformed necklace rings and q mobius function abstract we introduce a q deformation of the classical mobius function and investigate its properties in connection with q deformed truncated necklace rings also we study the strictly natural isomorphism of q deformed necklace rings

compact subsets of the first baire class perhaps the earliest results about pointwise compact sets of baire class 1 functions are the two selection theorems of e helly found in most of the standard texts on real variable see e g lo n these two theorems are really theorems about a particular example of a compact set of baire class 1 functions known today as helly space the space of all nondecreasing functions from the unit interval i 0 1 into itself more recently the notion of baire class 1 function turned out to also be important in some areas of functional analysis see r3 for example odell and rosenthal or showed that the double dual of a separable banach space e with the weak topology consists only of baire class 1 functions defined on the unit ball of e if and only if the space e contains no subspace isomorphic to 1 this resulted in a renewed interest in this class of spaces for example building on the work of rosenthal r2 bourgain fyemlin and talagrand bft proved analogues of the two theorems of helly for the whole first baire class using their results godefroy go showed that this class of spaces enjoys some interesting permanence properties for example if a compact space k is representable as a compact set of baire class 1 functions then so is p k the space of all radon probability measures on k with the weak topology some further permanence properties of this class of spaces were obtained by marciszewski ml m2 and an excellent survey of the early results is given by r pol po2 our paper is an attempt towards a fine structure theory of compact subsets of first baire class the first result that we give is a positive answer to a natural question one usually asks in such a context

borel extractions of converging sequences in compact sets of borel functions abstract it is well known by a classical result of bourgain fremlin talagrand that if k is a pointwise compact set of borel functions on a polish space then given any cluster point f of a sequence f n n in k one can extract a subsequence f n k k converging to f in the present work we prove that this extraction can be achieved in a borel way this will prove in particular that the notion of analytic subspace of a separable rosenthal compacta is absolute and does not depend on the particular choice of a dense sequence

constructing witt burnside rings abstract the witt burnside ring of a profinite group g over a commutative ring a generalizes both the burnside ring of virtual g sets and the rings of universal and p typical witt vectors over a the witt burnside ring of g over the monoid ring z m where m is a commutative monoid is proved isomorphic to the grothendieck ring of a category whose objects are almost finite g sets equipped with a map to m that is constant on g orbits in particular if a is a commutative ring and a denotes the set a as a monoid under multiplication then the witt burnside ring of g over z a is isomorphic to graham s ring of virtual g strings with coefficients in a this result forms the basis for a new construction of witt burnside rings and provides an important missing link between the constructions of dress and siebeneicher adv in math 70 1988 87 132 and graham adv in math 99 1993 248 263 with this approach the usual truncation frobenius verschiebung and teichmuller maps readily generalize to maps between witt burnside rings

decomposable functors and the exponential principle abstract we develop a combinatorial theory for the operation of forming the logarithm of generating functions associated with covariant functors on the category of finite sets and bijective maps this leads to a rather general and flexible exponential principle for labeled combinatorial structures we also introduce the concept of a topos like category which turns out to be a convenient framework for the discussion of a wide range of applications a few of which are studied in detail

generalized burnside grothendieck ring functor and aperiodic ring functor associated with profinite groups abstract for every profinite group g we construct two covariant functors g and ap g which are equivalent to the functor w g introduced in a dress c siebeneicher the burnside ring of profinite groups and the witt vectors construction adv math 70 1988 87 132 we call g the generalized burnside grothendieck ring functor and ap g the aperiodic ring functor associated with g in case g is abelian we also construct another functor ap g from the category of commutative rings with identity to itself as a generalization of the functor ap introduced in k varadarajan k wehrhahn aperiodic rings necklace rings and witt vectors adv math 81 1990 1 29 finally it is shown that there exist q analogues of these functors i e w g g ap g and ap g in case g is the profinite completion of the multiplicative infinite cyclic group c

on the subspaces of jf and jt with non separable dual it is proved that every subspace of james tree space jt with non separable dual contains an isomorph of james tree complemented in jt this yields that every complemented subspace of jt with non separable dual is isomorphic to jt a new jt like space denoted as tf is defined it is shown that every subspace of james function space jf with non separable dual contains an isomorph of tf the later yields that every subspace of jf with non separable dual contains isomorphs of c0 and lp for 2 p the analogues of the above results for bounded linear operators are also proved

necklace rings and logarithmic functions in this paper we develop the theory of the necklace ring and the logarithmic function regarding the necklace ring we introduce the necklace ring functor nr from the category of special rings into the category of special rings and then study the associated adams operators as far as the logarithmic function is concerned we generalize the results in bryant s paper free lie algebras and formal power series j algebra 253 1 2002 167 188 to the case of graded lie super algebras with a group action by applying the euler poincare principle

an application of burnside rings in elementary finite group theory abstract a canonical map from the burnside ring c of a finite cyclic group c into the burnside ring g of any finite group g of the same order is exhibited and it is shown that many results from elementary finite group theory in particular those claiming certain congruence relations are simple consequences of the existence of this map in addition it is shown that this map defines an isomorphism from c onto the subring 0 g of g consisting of those virtual g sets x which have the same number of invariants for every two subgroups u v of g of the same order if and only if g is nilpotent finally a rather natural extension to profinite groups is indicated

the burnside ring of profinite groups and the witt vector construction abstract the classical construction of witt vectors can be understood as a special case of a construction which can be defined relative to any given profinite group g in terms of its completed burnside ring lde g it specializes to the classical situation in case g is infinite cyclic

the representation ring of the quantum double of a finite group abstract we present some results about the representation ring of the quantum double of a finite group over fields of arbitrary characteristic we give a direct sum decomposition of this representation ring into ideals involving green rings of subgroups given characters of such green rings we construct characters of the representation ring of the quantum double and show that all characters arise in this fashion we prove that the characters thereby obtained from brauer characters separate modules of the quantum double up to composition factors

a generalization of the dress construction for a tambara functor and its relation to polynomial tambara functors abstract for a finite group g semi mackey functors and semi tambara functors are regarded as g bivariant analogs of semi groups and semi rings respectively in fact if g is trivial they agree with the ordinary semi groups and semi rings and many naive algebraic properties concerning rings and groups have been extended to these g bivariant analogous notions in this article we investigate a g bivariant analog of the semi group rings with coefficients just as a coefficient ring r and a monoid q yield the semi group ring r q our construction enables us to make a tambara functor t m out of a semi mackey functor m and a coefficient tambara functor t this construction is a composant of the tambarization and the dress construction as expected this construction is the one uniquely determined by the righteous adjoint property besides in analogy with the trivial group case if m is a mackey functor then t m is equipped with a natural hopf structure moreover as an application of the above construction we also obtain some g bivariant analogs of the polynomial rings

axiomatic theory of burnside rings i abstract in this paper we study abstract burnside rings of essentially finite categories under unique epi mono factorization property and the existence of coequalizers for some kind we prove the existence of a fundamental exact sequence for abr furthermore an abr can be embedded into a direct product of rational character rings

the hochschild cohomology ring of a group algebra there is a standard additive decomposition of the hochschild cohomology ring of the group algebra of a finite group g as the direct sum of the cohomology rings of the centralizers of representatives of the conjugacy classes of g a special case of our main result describes the cup product in terms of this decomposition as applications we determine presentations for the hochschild cohomology rings of 1 the mod 3 group algebra of the symmetric group s 3 2 the mod 2 group algebra of the alternating group a 4 and 3 the mod 2 group algebras of the dihedral 2 groups

the tambara structure of the trace ideal for cyclic extensions abstract this paper explores the tambara functor structure of the trace ideal of a galois extension in the case of a pro cyclic extension we are able to explicitly determine the generators of the ideal furthermore we show that the absolute trace ideal of a cyclic group is strongly principal when viewed as an ideal of the burnside tambara functor applying our results we calculate the trace ideal for extensions of finite fields the appendix determines a formula for the norm of a quadratic form over an arbitrary finite extension of a finite field

on the fractions of semi mackey and tambara functors for a finite group g a semi mackey resp tambara functor is regarded as a g bivariant analog of a commutative monoid resp ring as such some naive algebraic constructions are generalized to this g bivariant setting in this article as a g bivariant analog of the fraction of a ring we consider fraction of a tambara and a semi mackey functor by a multiplicative semi mackey subfunctor

unconditional families in banach spaces it is shown that for every separable banach space x with non separable dual the space x contains an unconditional family of size x the proof is based on ramsey theory for trees and finite products of perfect sets of reals among its consequences it is proved that every dual banach space has a separable quotient

the burnside ring of the infinite cyclic group and its relations to the necklace algebra λ rings and the universal ring of witt vectors abstract it is shown that well known product decompositions of formal power series arise from combinatorially defined canonical isomorphisms between the burnside ring of the infinite cyclic group on the one hand and grothendieck s ring of formal power series with constant term 1 as well as the universal ring of witt vectors on the other hand

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12