### Abstract

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

pagine (da-a) | 1765-1785 |

Numero di pagine | 21 |

Rivista | Journal of Pure and Applied Algebra |

Volume | 222 |

Stato di pubblicazione | Published - 2018 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cita questo

*Journal of Pure and Applied Algebra*,

*222*, 1765-1785.

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

Risultato della ricerca: Article

*Journal of Pure and Applied Algebra*, vol. 222, pagg. 1765-1785.

}

TY - JOUR

T1 - Minimal star-varieties of polynomial growth and bounded colength

AU - La Mattina, Daniela

AU - Do Nascimento, Thais Silva

AU - Vieira, Ana Cristina

PY - 2018

Y1 - 2018

N2 - 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.

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.

UR - http://hdl.handle.net/10447/297410

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

M3 - Article

VL - 222

SP - 1765

EP - 1785

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

ER -