Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897552 | Journal of Pure and Applied Algebra | 2018 | 18 Pages |
Abstract
Let V be a variety of associative algebras with involution â over a field F of characteristic zero. Giambruno and Mishchenko proved in [6] that the â-codimension sequence of V is polynomially bounded if and only if V does not contain the commutative algebra D=FâF, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4Ã4 upper triangular matrices, endowed with the reflection involution. As a consequence the algebras D and M generate the only varieties of almost polynomial growth. In [20] the authors completely classify all subvarieties and all minimal subvarieties of the varieties varâ(D) and varâ(M). In this paper we exhibit the decompositions of the â-cocharacters of all minimal subvarieties of varâ(D) and varâ(M) and compute their â-colengths. Finally we relate the polynomial growth of a variety to the â-colengths and classify the varieties such that their sequence of â-colengths is bounded by three.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Daniela La Mattina, Thais Silva do Nascimento, Ana Cristina Vieira,