Trace identities and almost polynomial growth

Daniela La Mattina, Antonio Ioppolo, Plamen Koshlukov, Antonio Ioppolo

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1 Citation (Scopus)


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: D2, the algebra of 2×2 diagonal matrices and C2, the algebra of 2×2 matrices generated by e11+e22 and e12. 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.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Pure and Applied Algebra
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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