Isomorphisms of Simple Lie Rings

Continuity of Lie Isomorphisms of Banach Algebras

We prove that if A and B are semisimple Banach algebras, then the separating subspace of every Lie isomorphism from A onto B is contained in the centre of B. Over the years, there has been considerable effort made and success in studying the structure of Lie isomorphisms of rings and Banach algebras [2–5, 7–15]. We are interested in investigating the continuity of Lie isomorphisms of Banach alg...

Lie and Jordan Structures in Simple, Associative Rings

Isomorphisms of p-adic group rings

A long-standing problem, first posed by Graham Higman [15] and later by Brauer [4] is the “isomorphism problem for integral group rings.” Given finite groups G and H, is it true that ZG = ZH implies G 2: H? Many authors have worked on this question, but progress has been difficult [30]. Perhaps the best positive result was that of Whitcomb in 1968 [37], who showed that the implication G = H hol...

Representation Rings of Lie Superalgebras

Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring RZ2(g) of virtual g-supermodules, up to (even) isomorphisms. In particular, we consider the ideal R+(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity rever...

Locally finite basic classical simple Lie superalgebras

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.