Polynomial codimension growth of algebras with involutions and superinvolutions

Daniela La Mattina, Antonio Ioppolo

Risultato della ricerca: Article

9 Citazioni (Scopus)

Abstract

Let A be an associative algebra over a field F of characteristic zero endowed with a graded involution or a superinvolution ∗ and let c^∗_n(A) be its sequence of ∗-codimensions. In [4,12]it was proved that if A is finite dimensional such sequence is polynomially bounded if and only if A generates a variety not containing a finite number of ∗-algebras: the groupalgebra of Z_2 and a 4-dimensional subalgebra of the 4 × 4 upper triangular matrices with suitable graded involutions or superinvolutions.In this paper we focus our attention on such algebras since they are the only finite dimensional ∗-algebras, up to T^∗_2 -equivalence, generating varieties of almost polynomialgrowth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth. We classify the subvarieties of such varieties by giving a complete list ofgenerating finite dimensional ∗-algebras. Along the way we classify all minimal varieties of polynomial growth and surprisingly we show that their number is finite for anygiven growth. Finally we describe the ∗-algebras whose ∗-codimensions are bounded by a linear function.
Lingua originaleEnglish
pagine (da-a)519-545
Numero di pagine27
RivistaDefault journal
Stato di pubblicazionePublished - 2017

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Involution
Codimension
Polynomial Growth
Finite Dimensional Algebra
Algebra
Polynomial
Classify
Upper triangular matrix
Associative Algebra
Exponential Growth
Linear Function
Subalgebra
Equivalence
If and only if
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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Polynomial codimension growth of algebras with involutions and superinvolutions. / La Mattina, Daniela; Ioppolo, Antonio.

In: Default journal, 2017, pag. 519-545.

Risultato della ricerca: Article

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