Skip to main content
Passa alla visualizzazione normale.

DANIELA LA MATTINA

Minimal star-varieties of polynomial growth and bounded colength

  • Authors: La Mattina, Daniela; do Nascimento, Thais Silva; Vieira, Ana Cristina*
  • Publication year: 2018
  • Type: Articolo in rivista (Articolo in rivista)
  • OA Link: http://hdl.handle.net/10447/297410

Abstract

Let V be a variety of associative algebras with involution * over a field F of characteristic zero. Giambruno and Mishchenko proved in that the *-codimension sequence of V is polynomially bounded if and only if V does not contain the commutative algebra D=F⊕F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4×4 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 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.