Search results for " 16R30"

showing 3 items of 3 documents

Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras

2012

The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.

Classical Invariant Theory05A15 05E05 05E10 13A50 15A72 16R10 16R30 20G05MacMahon Partition AnalysisHilbert SeriesRational symmetric functions classical invariant theory algebras with polynomial identity cocharacter sequenceMathematics - Rings and AlgebrasCommutative Algebra (math.AC)Mathematics - Commutative AlgebraRational Symmetric FunctionsAlgebras with Polynomial IdentitySettore MAT/02 - AlgebraRings and Algebras (math.RA)Noncommutative Invariant TheoryFOS: MathematicsCocharacter SequenceMathematics - CombinatoricsCombinatorics (math.CO)
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Matrix algebras with degenerate traces and trace identities

2022

In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…

PolynomialAlgebra and Number TheoryTrace (linear algebra)Trace algebrasDiagonal matricesDegenerate energy levelsMathematics - Rings and AlgebrasType (model theory)Polynomial identitiesStirling numbersCombinatoricsMatrix (mathematics)Settore MAT/02 - Algebra16R10 16R30 16R50Rings and Algebras (math.RA)Diagonal matrixFOS: MathematicsDegenerate tracesAlgebra over a fieldCommutative propertyTrace algebras; Polynomial identities; Diagonal matrices; Degenerate traces; Stirling numbersMathematics
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Trace identities and almost polynomial growth

2021

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.

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)
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