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arXiv · 2012.10991

Trace identities and almost polynomial growth

Antonio Ioppolo·Plamen Koshlukov·Daniela La Mattina
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Abstract

In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.

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Antonio Ioppolo, Plamen Koshlukov, Daniela La Mattina. 2020-12-20. Trace identities and almost polynomial growth. https://doi.org/10.1016/j.jpaa.2020.106501

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