Lie Isomorphisms of Primitive 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...

Quasi-Primitive Rings and Density Theory

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...

Isomorphisms and Automorphisms of Universal Heffalump Lie Algebras

The classification of a family of infinite dimensional Lie algebras is carried out, and a determination of their automorphism groups, in certain cases is supplied. Introduction. The theory of finite dimensional simple Lie algebras over algebraically closed fields of characteristic zero achieves a classification of such algebras and a description of their automorphism groups (see [4]). To these ...