Varieties of algebras with pseudoinvolution and polynomial growth

Ioppolo, Antonio; Martino, Fabrizio

doi:10.1080/03081087.2017.1394257

Cited by 11 publications

(3 citation statements)

References 18 publications

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“…Similar results about codimension sequence and polynomial growth for associative algebras were given by several authors in various settings, such as superalgebras ( [7]), algebras graded by a finite abelian group ( [24]), algebras with involution ( [6]), superinvolution ( [5]) and pseudoinvolution ( [19]).…”

Section: Introductionsupporting

confidence: 77%

Varieties of special Jordan algebras of almost polynomial growth

Martino

2019

Journal of Algebra

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Section: Introductionsupporting

confidence: 77%

Varieties of special Jordan algebras of almost polynomial growth

Martino

2019

Journal of Algebra

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“…Varieties of poylnomial growth were extensively studied in the past years in various settings. We refer the interested reader to [5], [6], [22] for some results about ordinary algebras; to [8], [23], [24], [32] for superalgebras and more generally group graded algebras; to [3], [7], [10], [20], [21], [25] for algebras with involution, graded involution, superinvolution and pseudoinvolution; to [27] for special Jordan algebras.…”

Section: Introductionmentioning

confidence: 99%

Differential identities and varieties of almost polynomial growth

Martino

Rizzo

2022

Isr. J. Math.

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Let V be an L-variety of associative L-algebras, i.e., algebras where a Lie algebra L acts on them by derivations, and let c L n (V), n ≥ 1, be its L-codimension sequence. If V is generated by a finite dimensional L-algebra, then such a sequence is polynomially bounded if and only if V does not contain U T 2 , the 2 × 2 upper triangular matrix algebra with trivial L-action, and U T ε 2 where L acts on U T 2 as the 1-dimensional Lie algebra spanned by the inner derivation ε induced by e 11 . In this paper we completely classify all the L-subvarieties of var L (U T 2 ) and var L (U T ε2 ) by giving a complete list of finite dimensional L-algebras generating them.

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“…We recall here that similar descriptions for the ordinary codimensions can be found in [14,Theorem 7.2.7] where it was proved that the only two varieties of (ordinary) algebras of almost polynomial growth are the ones generated by the Grassmann algebra E and by U T 2 . In the case of algebras with involution, superinvolution, pseudoinvolution or graded by a finite group, a complete list of varieties of algebras of almost polynomial growth was exihibited in [5,6,9,10,18,19,20,29].…”

Section: Introductionmentioning

confidence: 99%

Trace identities and almost polynomial growth

Ioppolo

Koshlukov

Mattina

2021

Journal of Pure and Applied Algebra

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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 × 2 diagonal matrices and C 2 , the algebra of 2 × 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.

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Varieties of algebras with pseudoinvolution and polynomial growth

Cited by 11 publications

References 18 publications

Varieties of special Jordan algebras of almost polynomial growth

Varieties of special Jordan algebras of almost polynomial growth

Differential identities and varieties of almost polynomial growth

Trace identities and almost polynomial growth

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