Minimal star-varieties of polynomial growth and bounded colength

作者：La Mattina Daniela; do Nascimento Thais Silva; Vieira Ana Cristina^*

来源：Journal of Pure and Applied Algebra, 2018, 222(7): 1765-1785.

DOI：10.1016/j.jpaa.2017.08.005

Let nu be a variety of associative algebras with involution * over a field F of characteristic zero. Giambruno and Mishchenko proved in [6] that the *-codimension sequence of nu is polynomially bounded if and only if nu does not contain the commutative algebra D = F circle plus F endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 x 4 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 var* (D) and var* (M). In this paper we exhibit the decompositions of the *-cocharacters of all minimal subvarieties of var* (D) and var* (M) and compute their *-colengths. Finally we relate the polynomial growth of a variety to the *-colengths and classify the varieties such that their sequence of *-colengths is bounded by three.

• 出版日期2018-7