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 (February 2021)) [10.1016/j.jpaa.2020.106501].
Trace identities and almost polynomial growth
Ioppolo A.
;
2021
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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