### Abstract

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

pagine (da-a) | 519-545 |

Numero di pagine | 27 |

Rivista | Journal of Algebra |

Stato di pubblicazione | Published - 2017 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cita questo

*Journal of Algebra*, 519-545.

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

Risultato della ricerca: Article

*Journal of Algebra*, pagg. 519-545.

}

TY - JOUR

T1 - Polynomial codimension growth of algebras with involutions and superinvolutions

AU - La Mattina, Daniela

AU - Ioppolo, Antonio

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/208896

M3 - Article

SP - 519

EP - 545

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -