Graded identities of some simple Lie superalgebras

Abstract

We study ${\mathbb{Z}}_2$-graded identities of Lie superalgebras of the type $b(t),t\ge 2$, over a field of characteristic zero. Our main result is that the $n$-th codimension is strictly less than $(\dim b(t){)}^n$ asymptotically. As a consequence we obtain an upper bound for ordinary (non-graded) PI-exponent for each simple Lie superalgebra $b(t),t\ge 3$.

References in corpus (1)

• A four-dimensional simple algebra with fractional PI-exponent

Cited by in corpus (5)

• Graded codimensions of Lie superalgebra $b(2)$
• Graded PI-exponents of simple Lie superalgebras
• Pauli gradings on Lie superalgebras and graded codimension growth
• Identities of graded simple algebras
• Codimensions of identities of solvable Lie superalgebras