6533b837fe1ef96bd12a3155

RESEARCH PRODUCT

Trace identities and almost polynomial growth

Plamen KoshlukovDaniela La MattinaAntonio Ioppolo

subject

PolynomialPure mathematicsTrace (linear algebra)Trace algebrasField (mathematics)01 natural sciencesPolynomial identitiesMatrix (mathematics)16R10 16R30 16R50Polynomial identitieCodimensions growth Polynomial identities Trace algebras0103 physical sciencesDiagonal matrixFOS: Mathematics0101 mathematicsCommutative propertyMathematicsCodimensions growth; Polynomial identities; Trace algebrasAlgebra and Number TheoryCodimensions growth010102 general mathematicsTrace algebraMathematics - Rings and AlgebrasExponential functionSettore MAT/02 - AlgebraRings and Algebras (math.RA)010307 mathematical physicsVariety (universal algebra)

description

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.

yearjournalcountryeditionlanguage
2021-01-01
10.1016/j.jpaa.2020.106501http://hdl.handle.net/10447/453717