### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 246-262 |

Numero di pagine | 17 |

Rivista | Journal of Pure and Applied Algebra |

Volume | 220 |

Stato di pubblicazione | Published - 2016 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cita questo

*Journal of Pure and Applied Algebra*,

*220*, 246-262.

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

Risultato della ricerca: Article

*Journal of Pure and Applied Algebra*, vol. 220, pagg. 246-262.

}

TY - JOUR

T1 - Polynomial growth and star-varieties

AU - Martino, Fabrizio

AU - La Mattina, Daniela

AU - Martino, Fabrizio

PY - 2016

Y1 - 2016

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

ER -