Search results for "T-ideal"
showing 5 items of 5 documents
Some varieties of algebras of polynomial growth
2008
We determine a complete list of finite dimensional algebras generating the subvarieties of var(G) and var(UT_2).
PI-algebras with slow codimension growth
2005
Let $c_n(A),\ n=1,2,\ldots,$ be the sequence of codimensions of an algebra $A$ over a field $F$ of characteristic zero. We classify the algebras $A$ (up to PI-equivalence) in case this sequence is bounded by a linear function. We also show that this property is closely related to the following: if $l_n(A), \ n=1,2,\ldots, $ denotes the sequence of colengths of $A$, counting the number of $S_n$-irreducibles appearing in the $n$-th cocharacter of $A$, then $\lim_{n\to \infty} l_n(A)$ exists and is bounded by $2$.
Varieties of almost polynomial growth: classifying their subvarieties
2007
Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).
Classifying the Minimal Varieties of Polynomial Growth
2014
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.
Varieties of algebras of polynomial growth
2008
Let V be a proper variety of associative algebras over a field F of characteristic zero. It is well-known that V can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of var(G) and var(UT 2), where G is the Grassmann algebra and UT2 is the algebra of 2 x 2 upper triangular matrices.