Search results for " *-codimensions"

showing 5 items of 5 documents

Polynomial growth and identities of superalgebras and star-algebras

2009

Abstract We study associative algebras with 1 endowed with an automorphism or antiautomorphism φ of order 2, i.e., superalgebras and algebras with involution. For any fixed k ≥ 1 , we construct associative φ -algebras whose φ -codimension sequence is given asymptotically by a polynomial of degree k whose leading coefficient is the largest or smallest possible.

Discrete mathematicsInvolution (mathematics)Settore MAT/02 - AlgebraPure mathematicsAlgebra and Number TheoryCodimensionAutomorphismAssociative property\varphi$-identity $T^\varphi$-ideal $\varphi$-codimensions growthMathematicsJournal of Pure and Applied Algebra
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Algebras with involution with linear codimension growth

2006

AbstractWe study the ∗-varieties of associative algebras with involution over a field of characteristic zero which are generated by a finite-dimensional algebra. In this setting we give a list of algebras classifying all such ∗-varieties whose sequence of ∗-codimensions is linearly bounded. Moreover, we exhibit a finite list of algebras to be excluded from the ∗-varieties with such property. As a consequence, we find all possible linearly bounded ∗-codimension sequences.

Discrete mathematicsPure mathematicsJordan algebraAlgebra and Number TheoryNon-associative algebraSubalgebraQuadratic algebra∗-CodimensionsSettore MAT/02 - AlgebraInterior algebra*-polynomial identity T*-ideal *-codimensions.∗-Polynomial identityT∗-idealDivision algebraAlgebra representationNest algebraMathematics
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On Codimensions of Algebras with Involution

2020

Let A be an associative algebra with involution ∗ over a field F of characteristic zero. One associates to A, in a natural way, a numerical sequence \(c^{\ast }_n(A),\)n = 1, 2, …, called the sequence of ∗-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A. In this paper we focus our attention on \(c^{\ast }_n(A),\)n = 1, 2, …, by presenting some recent results about it.

Polynomial (hyperelastic model)CombinatoricsSequenceSettore MAT/02 - Algebra*-identitiesAssociative algebraZero (complex analysis)Involution (philosophy)Field (mathematics)*-codimensionsGrowthMathematics
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Polynomial codimension growth of graded algebras

2009

We study associative $G$-graded algebras with 1 of polynomial $G$-codimension growth, where $G$ is a finite group. For any fixed $k\geq 1,$ we construct associative $G$-graded algebras of upper triangular matrices whose $G$-codimension sequence is given asymptotically by a polynomial of degree $k$ whose leading coefficient is the largest or smallest possible.

Settore MAT/02 - AlgebraGraded algebra graded identity G-codimensionsGroups, Rings and Group Rings
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Supervarieties and *-varieties of algebras of polynomial growth

2008

We study the sequence of supercodimensions and *-codimensions of unitary algebras.

supercodimensions *-codimensions
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