Identities of graded simple algebras

Abstract

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