Let F be a field of characteristic zero, L a Lie algebra over F, and A an L-algebra – that is, an associative algebra over F with an action of L induced by derivations. This action of L on A can be extended to an action of its universal enveloping algebra U(L), leading to the concept of L-identities or differential identities of A: polynomials in variables xu:= u(x), where u ∈ U(L), that vanish under all substitutions of elements from A. Differential identities were first introduced by Kharchenko in 1978, and, in later years, subsequent work by Gordienko and Kochetov has spurred a renewed interest in both their structure and quantitative properties. In this talk, I will present recent results on the differential identities of matrix L-algebras, with a particular focus on their classification and growth behaviour.
This video is part of the European Non-Associative Algebra Seminar series.
