Polynomial growth and star-varieties

Risultato della ricerca: Article

8 Citazioni (Scopus)

Abstract

Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c_n*(V), n= 1, 2, . ., be its *-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F⊕ F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 ×4 upper triangular matrices. Such algebras generate the only varieties of *-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the *-varieties of almost polynomial growth by giving a complete list of finite dimensional *-algebras generating them.
Lingua originaleEnglish
pagine (da-a)246-262
Numero di pagine17
RivistaJournal of Pure and Applied Algebra
Volume220
Stato di pubblicazionePublished - 2016

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Polynomial Growth
Involution
Star
Variety of Algebras
Algebra
Upper triangular matrix
Associative Algebra
Commutative Algebra
Finite Dimensional Algebra
Exponential Growth
Codimension
Subalgebra
Classify
If and only if
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cita questo

Polynomial growth and star-varieties. / Martino, Fabrizio; La Mattina, Daniela; Martino, Fabrizio.

In: Journal of Pure and Applied Algebra, Vol. 220, 2016, pag. 246-262.

Risultato della ricerca: Article

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T1 - Polynomial growth and star-varieties

AU - Martino, Fabrizio

AU - La Mattina, Daniela

AU - Martino, Fabrizio

PY - 2016

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N2 - Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c_n*(V), n= 1, 2, . ., be its *-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F⊕ F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 ×4 upper triangular matrices. Such algebras generate the only varieties of *-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the *-varieties of almost polynomial growth by giving a complete list of finite dimensional *-algebras generating them.

AB - Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c_n*(V), n= 1, 2, . ., be its *-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F⊕ F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 ×4 upper triangular matrices. Such algebras generate the only varieties of *-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the *-varieties of almost polynomial growth by giving a complete list of finite dimensional *-algebras generating them.

KW - Growth

KW - Star-codimensions

KW - Star-polynomial identities

UR - http://hdl.handle.net/10447/176239

UR - http://www.elsevier.com/locate/jpaa

M3 - Article

VL - 220

SP - 246

EP - 262

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

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