Rings of quotients of group algebras

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

On Fox Quotients of Arbitrary Group Algebras

For a group G and N-series G of G let In R,G(G), n ≥ 0, denote the filtration of the group algebra R(G) induced by G , and IR(G) its augmentation ideal. For subgroups H of G , left ideals J of R(H) and right H -submodules M of IZZ(G) the quotients IR(G)J/MJ are studied by homological methods, notably for M = IZZ(G)IZZ(H), IZZ(H)IZZ(G) + IZZ([H,G])ZZ(G) and ZZ(G)IZZ(N) + In ZZ,G(G) with N CG whe...

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...

Rings of Quotients of Rings of Functions

Algebras of Quotients of Path Algebras

Leavitt path algebras are shown to be algebras of right quotients of their corresponding path algebras. Using this fact we obtain maximal algebras of right quotients from those (Leavitt) path algebras whose associated graph satisfies that every vertex connects to a line point (equivalently, the Leavitt path algebra has essential socle). We also introduce and characterize the algebraic counterpa...