Identities of graded simple algebras

Abstract

We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$ we prove the existence of the graded PI-exponent, provided that $\Gamma$ is a commutative semigroup. If $A$ is simple in a non-graded sense the existence of the graded PI-exponent is proved without any restrictions on $\Gamma$.

References in corpus (3)

• Graded identities of some simple Lie superalgebras
• Graded codimensions of Lie superalgebra $b(2)$
• Graded PI-exponents of simple Lie superalgebras

Cited by in corpus (1)

• On $H$-simple not necessarily associative algebras