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=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 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.
|Numero di pagine||21|
|Rivista||Journal of Pure and Applied Algebra|
|Stato di pubblicazione||Published - 2018|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory