Minimal star-varieties of polynomial growth and bounded colength

Mattina, Daniela La; Nascimento, Thais Silva do; Vieira, Ana Cristina

doi:10.1016/j.jpaa.2017.08.005

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Classifying * -Algebras With Bounded Multiplicities Of the C...1

Introduction1

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2023

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Cited by 15 publications

(2 citation statements)

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“…We want to highlight that a similar result concerning algebras with ordinary polynomial identities was proved by Kemer in [18], by Vieira in [27] in the setting of superalgebras and in [20] for algebras with involution.…”

Section: Classifying * -Algebras With Bounded Multiplicities Of the C...supporting

confidence: 57%

On multiplicities of cocharacters for algebras with superinvolution

Ioppolo

Martino

2021

Journal of Pure and Applied Algebra

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Section: Classifying * -Algebras With Bounded Multiplicities Of the C...supporting

confidence: 57%

On multiplicities of cocharacters for algebras with superinvolution

Ioppolo

Martino

2021

Journal of Pure and Applied Algebra

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“…, is the dimension of the space of multilinear * -polynomials in n fixed variables in the corresponding relatively free algebra with involution of countable rank. Such sequence has been extensively studied (see [8,15,16,17,18,19] ) but it turns out that it can be explicitly computed only in very few cases. In case A is a PI-algebra, i.e, it satisfies a non trivial polynomial identity, it was proved in [9] that, as in the ordinary case, c * n (A), n = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

Codimensions of star-algebras and low exponential growth

Giambruno

Mattina

2020

Isr. J. Math.

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In this paper we prove that if A is any algebra with involution * satisfying a non trivial polynomial identity, then its sequence of * -codimensions is eventually non decreasing. Furthermore by making use of the * -exponent we reconstruct the only two * -algebras, up to T * -equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.

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