Codimension growth of two-dimensional non-associative algebras

Non Associative Linear Algebras

Non-associative algebras associated to Poisson algebras

Poisson algebras are usually defined as structures with two operations, a commutative associative one and an anti-commutative one that satisfies the Jacobi identity. These operations are tied up by a distributive law, the Leibniz rule. We present Poisson algebras as algebras with one operation, which enables us to study them as part of non-associative algebras. We study the algebraic and cohomo...

Simple Associative Conformal Algebras of Linear Growth

We describe simple finitely generated associative conformal algebras of Gel’fand–Kirillov dimension one.

Inner Derivations of Non-associative Algebras

In this note we propose a definition of inner derivation for nonassociative algebras. This definition coincides with the usual one for Lie algebras, and for associative algebras with no absolute right (left) divisor of zero. I t is well known that all derivations of semi-simple associative or Lie algebras over a field of characteristic zero are inner. Recent correspondence with N. Jacobson has ...

On the Codimension Growth of G-graded Algebras

Let W be an associative PI affine algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W ) and exp(We) denote the codimension growth of W and of the identity component We, respectively. We prove: exp(W ) ≤ |G| exp(We). This inequality had been conjectured by Bahturin and Zaicev.