AUGMENTATION QUOTIENTS OF INTEGRAL GROUP RINGS

Quotients of Representation Rings

We give a proof using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(∞)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to ∞. This in turn allows a detailed description of the quotient map in terms of a re...

Class Groups of Integral Group Rings(x)

Let A be an Ä-order in a semisimple finite dimensional /(-algebra, where K is an algebraic number field, and R is the ring of algebraic integers of K. Denote by C(A) the reduced class group of the category of locally free left A-lattices. Choose A= ZC, the integral group ring of a finite group G, and let A be a maximal Z-order in QG containing A. There is an epimorphism C(A)-C(A'), given by JIÍ...

Rings of Quotients of Rings of Functions

Commutative group rings with von Neumann regular total rings of quotients

Article history: Received 12 May 2011 Available online xxxx Communicated by Luchezar L. Avramov In memory of Miki Neumann

Central Units of Integral Group Rings of Nilpotent Groups

In this paper a finite set of generators is given for a subgroup of finite index in the group of central units of the integral group ring of a finitely generated nilpotent group. In this paper we construct explicitly a finite set of generators for a subgroup of finite index in the centre Z(U(ZG)) of the unit group U(ZG) of the integral group ring ZG of a finitely generated nilpotent group G. Ri...