Differential identities, almost polynomial growth and matrix algebras

Abstract: 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 $x^u := u(x)$, where $u \in U(L)$, 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 behavior.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar