Identities of *-superalgebras and almost polynomial growth

Abstract

We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.

Keywords:

• polynomial identity
• graded involution
• almost polynomial growth

AMS Subject Classifications:

• Primary: 16R50
• Secondary: 16R10
• 16P90
• 20C30

Acknowledgements

The authors would like to thank the referee for useful suggestions. The second author is also thankful to the Università di Palermo for its hospitality during his stay.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Partially support by CAPES – Coordenação de Aperfeiçoamento de Pessoal de Nível Superior [grant number 99999.014488/2013-02].