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Now showing items 117 of 17

Biset functors and brauer's induction theorem
(Bilkent University, 2014)We introduce two algebras on the endomorphism ring of the direct sum of character rings of groups from some collection. We prove the equality of these algebras to simplify a step in the proof of Brauer’s Induction Theorem. ... 
Blocks of quotients of mackey algebras
(Bilkent University, 2015)We review a theorem by Boltje and K¨ulshammer which states that under certain circumstances the endomorphism ring EndRG(RX) has only one block. We study the double Burnside ring, the Burnside ring and the transformations ... 
Canonical induction for trivial source rings
(Bilkent University, 2013)We discuss the canonical induction formula for some special Mackey functors by following the construction of Boltje. These functors are the ordinary and modular character rings and the trivial source rings. Making use ... 
A correspondence of simple alcahestic group functors
(Bilkent University, 2008)Representation theory of finite groups associates two classical constructions to a group G, namely the representation ring of G and the Burnside ring of G. These rings share a special structure that comes from three ... 
Fusion systems in group representation theory
(Bilkent University, 2013)Results on the Mackey category MF corresponding to a fusion system F and fusion systems defined on ppermutation algebras are our main concern. In the first part, we give a new proof of semisimplicity of MF over C by ... 
Green correspondence for Mackey functors
(Bilkent University, 2008)The Green corespondence for modules of group algebras was introduced by Green in 1964. A version for Mackey functors was introduced by Sasaki in 1982. Sasaki’s characterization of Mackey functor correspondence was based ... 
Inductions, restrictions, evaluations, and sunfunctors of Mackey functors
(Bilkent University, 2008) 
Mackey decomposition for Brauer pairs
(Bilkent University, 202008)For a ﬁnite group G and an algebraically closed ﬁeld k of characteristic p, a kalgebra A with a Gaction is called a Galgebra. A pair (P,c) such that P is a psubgroup of G and c is a block idempotent of the Galgebra ... 
Mackey group categories and their simple functors
(Bilkent University, 2012)Constructing the Mackey group category M using axioms which are reminiscent of fusion systems, the simple RMfunctors (the simple functors from the Rlinear extension of M to Rmodules, where R is a commutative ring) can ... 
Modular representations and monomial burnside rings
(Bilkent University, 2004)We introduce canonical induction formulae for some character rings of a finite group, some of which follows from the formula for the complex character ring constructed by Boltje. The rings we will investigate are the ... 
The monomial Burnside functor
(Bilkent University, 2009)Given a finite group G, we can realize the permutation modules by the linearization map defined from the Burnside ring B(G) to the character ring of G, denoted AK(G). But not all KGmodules are permutation modules. To ... 
On monomial Burnside rings
(Bilkent University, 2003)This thesis is concerned with some different aspects of the monomial Burnside rings, including an extensive, self contained introduction of the A−fibred G−sets, and the monomial Burnside rings. However, this work has two ... 
On some of the simple composition factors of the biset functor of Ppermutation modules
(Bilkent University, 201607)Let k be an algebraically closed field of characteristic p, which is a prime, and C denote the field of complex numbers. Given a finite group G, letting ppk(G) denote the Grothendieck group of ppermutation kGmodules, we ... 
On the exponential map of the Burnside ring
(Bilkent University, 2002)We study the exponential map of the Burnside ring. We prove the equivalence of the three different characterizations of this map and examine the surjectivity in order to describe the elements of the unit group of the ... 
The pandemic fusion system for endomorphism algebras of ppermutation modules
(Bilkent University, 201809)During the 1980's Puig developed a new approach to modular representation theory, introducing new plocal invariants and thereby extending Green's work on Galgebras. We investigate the Puig category, commenting on its ... 
Real monomial Burnside rings and a decomposition of the the tom Dieck map
(Bilkent University, 2009)This thesis is mainly concerned with a decomposition of the reduced tom Dieck map die : f A(RG) → B(G) × into two maps die+ and die− of the real monomial Burnside ring. The key idea is to introduce a real Lefschetz ... 
Simple functors of admissible linear categories
(Bilkent University, 2013)We review the notion of an admissible Rlinear category for a commutative unital ring R and we prove the classification theorem for simple functors of such a category by BarkerBoltje which states that there is a bijective ...