### Abstract

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

pagine (da-a) | 221-233 |

Numero di pagine | 13 |

Rivista | Default journal |

Volume | 18 |

Stato di pubblicazione | Published - 2015 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cita questo

**Asymptotics for Graded Capelli Polynomials.** / Benanti, Francesca Saviella.

Risultato della ricerca: Article

*Default journal*, vol. 18, pagg. 221-233.

}

TY - JOUR

T1 - Asymptotics for Graded Capelli Polynomials

AU - Benanti, Francesca Saviella

PY - 2015

Y1 - 2015

N2 - The finite dimensional simple superalgebras play an important role in the theoryof PI-algebras in characteristic zero. The main goal of this paper is to characterize the T2-ideal of graded identities of any such algebra by considering the growth of the correspondingsupervariety. We consider the T2-ideal M+1,L+1 generated by the graded Capelli polynomialsCapM+1[Y,X] and CapL+1[Z,X] alternanting on M + 1 even variables and L + 1odd variables, respectively.We prove that the graded codimensions of a simple finite dimensionalsuperalgebra are asymptotically equal to the graded codimensions of the T2-ideal M+1,L+1, for some fixed natural numbers M and L. In particularcsupn ( k2+l2+1,2kl+1) csupn (Mk,l(F ))andcsupn ( s2+1,s2+1) csupn (Ms(F ⊕ tF)).These results extend to finite dimensional superalgebras a theorem of Giambruno andZaicev [6] giving in the ordinary case the asymptotic equalitycsupn ( k2+1,1) csupn (Mk(F ))between the codimensions of the Capelli polynomials and the codimensions of the matrixalgebra Mk(F ).

AB - The finite dimensional simple superalgebras play an important role in the theoryof PI-algebras in characteristic zero. The main goal of this paper is to characterize the T2-ideal of graded identities of any such algebra by considering the growth of the correspondingsupervariety. We consider the T2-ideal M+1,L+1 generated by the graded Capelli polynomialsCapM+1[Y,X] and CapL+1[Z,X] alternanting on M + 1 even variables and L + 1odd variables, respectively.We prove that the graded codimensions of a simple finite dimensionalsuperalgebra are asymptotically equal to the graded codimensions of the T2-ideal M+1,L+1, for some fixed natural numbers M and L. In particularcsupn ( k2+l2+1,2kl+1) csupn (Mk,l(F ))andcsupn ( s2+1,s2+1) csupn (Ms(F ⊕ tF)).These results extend to finite dimensional superalgebras a theorem of Giambruno andZaicev [6] giving in the ordinary case the asymptotic equalitycsupn ( k2+1,1) csupn (Mk(F ))between the codimensions of the Capelli polynomials and the codimensions of the matrixalgebra Mk(F ).

UR - http://hdl.handle.net/10447/100576

M3 - Article

VL - 18

SP - 221

EP - 233

JO - Default journal

JF - Default journal

ER -