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Abstract
In this paper, we study the growth of the codimensions of a finite dimensional -superalgebra
over a field of characteristic zero. We prove that
has polynomial growth if and only if any finite dimensional
-superalgebra satisfying the same
-graded identities of
has an explicit decomposition into suitable
-superalgebras. We also give such a characterization by studying the decomposition of the
-cocharacter of
. In this case, the main tool is the representation theory of the product of symmetric groups.
AMS Subject Classifications:
Acknowledgements
The authors would like to thank the referee for useful suggestions.
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].