### Abstract

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

pagine (da-a) | 961-976 |

Numero di pagine | 16 |

Rivista | Algebras and Representation Theory |

Volume | 22 |

Stato di pubblicazione | Published - 2019 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cita questo

*Algebras and Representation Theory*,

*22*, 961-976.

**Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions.** / La Mattina, Daniela; Giambruno, Antonino; Ioppolo, Antonio.

Risultato della ricerca: Article

*Algebras and Representation Theory*, vol. 22, pagg. 961-976.

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TY - JOUR

T1 - Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions

AU - La Mattina, Daniela

AU - Giambruno, Antonino

AU - Ioppolo, Antonio

PY - 2019

Y1 - 2019

N2 - Let A be a superalgebra with graded involution or superinvolution ∗ and let cn∗(A), n = 1,2,…, be its sequence of ∗-codimensions. In case A is finite dimensional, in Giambruno et al. (Algebr. Represent. Theory 19(3), 599–611 2016, Linear Multilinear Algebra 64(3), 484–501 2016) it was proved that such a sequence is polynomially bounded if and only if the variety generated by A does not contain the group algebra of ℤ2 and a 4-dimensional subalgebra of the 4 × 4 upper-triangular matrices with suitable graded involutions or superinvolutions. In this paper we study the general case of ∗-superalgebras satisfying a polynomial identity. As a consequence we classify the varieties of ∗-superalgebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth, and we give a full classification of their subvarieties which was started in Ioppolo and La Mattina (J. Algebra 472, 519–545 2017)

AB - Let A be a superalgebra with graded involution or superinvolution ∗ and let cn∗(A), n = 1,2,…, be its sequence of ∗-codimensions. In case A is finite dimensional, in Giambruno et al. (Algebr. Represent. Theory 19(3), 599–611 2016, Linear Multilinear Algebra 64(3), 484–501 2016) it was proved that such a sequence is polynomially bounded if and only if the variety generated by A does not contain the group algebra of ℤ2 and a 4-dimensional subalgebra of the 4 × 4 upper-triangular matrices with suitable graded involutions or superinvolutions. In this paper we study the general case of ∗-superalgebras satisfying a polynomial identity. As a consequence we classify the varieties of ∗-superalgebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth, and we give a full classification of their subvarieties which was started in Ioppolo and La Mattina (J. Algebra 472, 519–545 2017)

UR - http://hdl.handle.net/10447/371736

UR - https://link.springer.com/article/10.1007/s10468-018-9807-3

M3 - Article

VL - 22

SP - 961

EP - 976

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

ER -