The group ring of SL 2 ( p 2 ) over the p - adic integers

The group ring of SL 2 ( 2 f ) over 2 - adic integers

Let R = Z 2 2 f ?1 ] and G = SL 2 (2 f). The group ring RG is calculated nearly up to Morita equivalence. In particular the irreducible RG-lattices can be described purely combinatorically in terms of subsets of f1 The group G = SL 2 (p f) of all 22-matrices over the eld k with p f elements is one of the simplest examples of a nonabelian nite group of Lie type. Its representation theory in char...

The Group Ring of Sl 2 (p F P-adic Integers for P Odd

Let p > 2 be a prime, The group ring RG is calculated nearly up to Morita equivalence: The projections of RG into the simple components of KG are given explicitly and the endomorphism rings and homomorphism bimodules between the projective indecomposable RG-lattices are described.

Liapunov Stability and the ring of P -adic integers

It is well-known that stable Cantor sets are topologically conjugate to adding machines. In this work we show are also conjugate to an algebraic object, the ring of P−adic integers with respect to group tramnslation. This ring is closely related to the field of p-adic numbers; connections and distintions are explored. The inverse limit construction provides a purely dynamical proof of an algebr...

An Isomorphism Between the P-adic Integers and a Ring Associated with a Tiling of N-space By Permutohedra

The classical lattice A ,*, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBT, in a natural way as a quotient ring of Z [xl. The ring GBT, can also be considered as the set of all finite sequences sO sl.. . sk, with si E GBT,/srGBT, for all i, where M is an appropriately chosen element in GBT,. The extended generalized ba...

Group Rings over the p-Adic Integers