Contributions to the theory of induced representations

  title={Contributions to the theory of induced representations},
  author={A. Dress},
Cohomology of G-Green Functors
In this paper, our goal is to develop the equivariant version of Hochschild cohomology. Here we develop a cohomology theory for Green functors. Mathematics Subject Classification: 16E30, 16E40
On passage to over-groups of finite indices of the Farrell-Jones conjecture
We use the controlled algebra approach to study the problem that whether the Farrell-Jones conjecture is closed under passage to over-groups of finite indices. Our study shows that this problem isExpand
The main conjecture of Iwasawa theory for totally real fields
Let p be an odd prime. Let $\mathcal{G}$ be a compact p-adic Lie group with a quotient isomorphic to ℤp. We give an explicit description of K1 of the Iwasawa algebra of $\mathcal{G}$ in terms ofExpand
Kernels, inflations, evaluations, and imprimitivity of Mackey functors
Abstract Let M be a Mackey functor for a finite group G. By the kernel of M we mean the largest normal subgroup N of G such that M can be inflated from a Mackey functor for G / N . We first studyExpand
Induction Theorems and Isomorphism Conjectures for K- and L-Theory
Abstract The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the algebraic K- and L-theory of the group ring and the topological K-theory of the reduced group C*-algebra of aExpand
Burnside rings
1 Let G be a finite group. The Burnside ring B(G) of the group G is one of the fundamental representation rings of G, namely the ring of permutation representations. It is in many ways the universalExpand
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 canonicalExpand
Canonical induction for trivial source rings
Ankara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2013.
Induction Categories for Compact Lie Groups
We use Euler groups to construct induction categories for Lie groups and suitable families of closed subgroups. Euler groups are universal additive invariants. Induction categories combine ordinaryExpand
Defect Theory for Prime Ideals and Dress"s Induction Theorem
It is due to Thévenaz that a large part of Puig"s theory of pointed groups carries over to the context of Green functors for finite groups, where here maximal ideals play the role of points in theExpand


A note on Witt rings
This note contains some applications of the theory of Mackey functors (cf. [3], [4] and [5]) to the study of Witt rings. A detailed version may be found in [3, Appendices A and B]. So let R be aExpand
Equivariant homology and Mackey functors
Induction and structure theorems for Grothendieck and Witt rings of orthogonal representations of finite groups
The Grothendieckand Wittring of orthogonal representations of a finite group is defined and studied. The main application (only indicated) is the reduction of the computation of Wall's variousExpand
Vertices of integral representations
0. The following is an outline of a theory of 11-projective RG-modules, where R is a ring, G a finite group and !1 a family of subgroups of G. The first section contains the obvious generalisationsExpand
A characterisation of solvable groups
Let G be a finite group. A G-set M is a finite set on which G operates from the left by permutations, i.e. a finite set together with a map G • (g, m) ~ g m with g(h m)= (g h) m, e m = m for g, h, eeExpand
Monomial representations under integral similarity
If u : (I,..., n) -+ [I)..., n) is a permutation, then we can represent (I as a permutation matrix ii = (6i,Vo~). Then cr 0 u’ = ab. If now T is a group and u is a permutational representation of T,Expand
On integral representations