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.
Ioppolo A., Koshlukov P., La Mattina D. (2021). Trace identities and almost polynomial growth. JOURNAL OF PURE AND APPLIED ALGEBRA, 225(2), 1-20 [10.1016/j.jpaa.2020.106501].
Trace identities and almost polynomial growth
Ioppolo A.;La Mattina D.
2021-01-01
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: 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.
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