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arXiv · 1701.01577

Identities of graded simple algebras

Dušan D. Repovš·Mikhail V. Zaicev
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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 $\Gamma$.

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Dušan D. Repovš, Mikhail V. Zaicev. 2017-01-06. Identities of graded simple algebras. https://doi.org/10.1080/03081087.2016.1167160

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