Varieties of Algebras with Superinvolution of Almost Polynomial Growth

Risultato della ricerca: Article

13 Citazioni (Scopus)

Abstract

Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let c_n∗(A) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
Lingua originaleEnglish
pagine (da-a)599-611
Numero di pagine13
RivistaDefault journal
Volume19
Stato di pubblicazionePublished - 2016

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Variety of Algebras
Polynomial Growth
Codimension
Associative Algebra
If and only if
Algebra
Polynomial
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cita questo

Varieties of Algebras with Superinvolution of Almost Polynomial Growth. / Giambruno, Antonino; La Mattina, Daniela; Ioppolo, Antonio.

In: Default journal, Vol. 19, 2016, pag. 599-611.

Risultato della ricerca: Article

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abstract = "Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let c_n∗(A) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.",
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AU - La Mattina, Daniela

AU - Ioppolo, Antonio

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N2 - Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let c_n∗(A) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.

AB - Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let c_n∗(A) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.

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KW - Polynomial identity

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