Minimal star-varieties of polynomial growth and bounded colength

Daniela La Mattina, Thais Silva Do Nascimento, Ana Cristina Vieira

Risultato della ricerca: Article

3 Citazioni (Scopus)

Abstract

Let V be a variety of associative algebras with involution * over a field F of characteristic zero. Giambruno and Mishchenko proved in that the *-codimension sequence of V is polynomially bounded if and only if V does not contain the commutative algebra D=FâF, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4Ã4 upper triangular matrices, endowed with the reflection involution. As a consequence the algebras D and M generate the only varieties of almost polynomial growth. In the authors completely classify all subvarieties and all minimal subvarieties of the varieties var*(D) and var*(M). In this paper we exhibit the decompositions of the *-cocharacters of all minimal subvarieties of var*(D) and var*(M) and compute their *-colengths. Finally we relate the polynomial growth of a variety to the *-colengths and classify the varieties such that their sequence of *-colengths is bounded by three.
Lingua originaleEnglish
pagine (da-a)1765-1785
Numero di pagine21
RivistaJournal of Pure and Applied Algebra
Volume222
Stato di pubblicazionePublished - 2018

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Polynomial Growth
Involution
Star
Classify
Algebra
Upper triangular matrix
Associative Algebra
Commutative Algebra
Codimension
Subalgebra
If and only if
Decompose
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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Minimal star-varieties of polynomial growth and bounded colength. / La Mattina, Daniela; Do Nascimento, Thais Silva; Vieira, Ana Cristina.

In: Journal of Pure and Applied Algebra, Vol. 222, 2018, pag. 1765-1785.

Risultato della ricerca: Article

La Mattina, Daniela ; Do Nascimento, Thais Silva ; Vieira, Ana Cristina. / Minimal star-varieties of polynomial growth and bounded colength. In: Journal of Pure and Applied Algebra. 2018 ; Vol. 222. pagg. 1765-1785.
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AB - Let V be a variety of associative algebras with involution * over a field F of characteristic zero. Giambruno and Mishchenko proved in that the *-codimension sequence of V is polynomially bounded if and only if V does not contain the commutative algebra D=FâF, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4Ã4 upper triangular matrices, endowed with the reflection involution. As a consequence the algebras D and M generate the only varieties of almost polynomial growth. In the authors completely classify all subvarieties and all minimal subvarieties of the varieties var*(D) and var*(M). In this paper we exhibit the decompositions of the *-cocharacters of all minimal subvarieties of var*(D) and var*(M) and compute their *-colengths. Finally we relate the polynomial growth of a variety to the *-colengths and classify the varieties such that their sequence of *-colengths is bounded by three.

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