A characterization of algebras with polynomial growth of the codimensions

On the growth of the identities of algebras

On the Codimension Growth of Finite-Dimensional Lie Algebras

Abstract We study the exponential growth of the codimensions cn(L) of a finite-dimensional Lie algebra L over a field of characteristic zero. We show that if the solvable radical of L is nilpotent then lim n → ∞ c n ( L ) exists and is an integer.

Simple and semisimple Lie algebras and codimension growth

Classifying the Minimal Varieties of Polynomial Growth

Let $\mathcal{V}$ be a variety of associative algebras generated by an algebra with $1$ over a field of characteristic zero. This paper is devoted to the classification of the varieties $\mathcal{V}$ which are minimal of polynomial growth (i.e., their sequence of codimensions growth like $n^k$ but any proper subvariety grows like $n^t$ with $t 4$, the number of minimal varieties is at least $|F|$, the cardinality of the base field and we give a recipe of how to construct them.

Codimension growth of two-dimensional non-associative algebras

Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.

Group Actions and Asymptotic Behavior of Graded Polynomial Identities

Asymptotic growth of codimensions sequences of identities of associative algebras