0000000000372776
AUTHOR
Ana Cristina Vieira
Minimal star-varieties of polynomial growth and bounded colength
Abstract Let V 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 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 [20] the authors completely classify all subvarieties and all minimal subvarieties of the varieties var ⁎ ( D ) and var ⁎ ( M ) . In this paper we e…
Identities of *-superalgebras and almost polynomial growth
We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.