Group algebras and enveloping algebras with nonmatrix and semigroup identities

Abstract

Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity not satisfied by the algebra of all 2-by-2 matrices over K. Then we examine those R for which I satisfies a semigroup identity (that is, a polynomial identity which can be written as the difference of two monomials).

11 pages. Written in LaTeX2e

References in corpus (1)

• Associative algebras satisfying a semigroup identity

Cited by in corpus (4)

• Lie solvable enveloping algebras of characteristic two
• Non-Matrix Polynomial identity enveloping algebras
• Associative algebras satisfying a semigroup identity
• Enveloping algebras of restricted Lie superalgebras satisfying non-matrix polynomial identities