0000000000180860
AUTHOR
Manuela Pipitone
Polynomial identities on superalgebras and exponential growth
Abstract Let A be a finitely generated superalgebra over a field F of characteristic 0. To the graded polynomial identities of A one associates a numerical sequence {cnsup(A)}n⩾1 called the sequence of graded codimensions of A. In case A satisfies an ordinary polynomial identity, such sequence is exponentially bounded and we capture its exponential growth by proving that for any such algebra lim n→∞ c n sup (A) n exists and is a non-negative integer; we denote such integer by supexp(A) and we give an effective way for computing it. As an application, we construct eight superalgebras Ai, i=1,…,8, characterizing the identities of any finitely generated superalgebra A with supexp(A)>2 in the f…
ALGEBRAS WITH INVOLUTION WHOSE EXPONENT OF THE *-CODIMENSIONS IS EQUAL TO TWO
ABSTRACT Let be a finite dimensional algebra with involution over a field of characteristic zero. In studying the sequence of -codimensions of , the notion of the -PI-exponent of has recently been introduced. We characterize algebras with involution having -PI-exponent greater than two and those having -PI-exponent equal to two.