On superalgebras with pseudoautomorphism of polynomial codimension growth

Abstract

Let A be an associative superalgebra endowed with a pseudoautomorphism p. In this paper we generalize the Wedderburn-Malcev Theorem in this setting and we prove that the sequence of p-codimensions of A is polynomially bounded if and only if the variety generated by A does not contain the group algebra of ${\mathbb{Z}}_2$ and the algebra of 2 × 2 upper-triangular matrices with suitable pseudoautomorphisms.

Keywords:

• Codimension
• growth
• identity
• pseudoautomorphism
• superalgebra

2020 Mathematics Subject Classification:

• Primary: 16R10
• 16R50
• Secondary: 16W10
• 16W50

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