In this paper, it is proved that the ideal I_w of the weak polynomial identities of the superalgebra M_1,1(E) is generated by the proper polynomials [x_1, x_2, x_3] and [x_2, x_1 ][x_3, x_1 ][x_4, x_1]. This is proved for any infinite field F of characteristic different from 2. Precisely, if B is the subalgebra of the proper polynomials of F<X>, we determine a basis and the dimension of any multihomogeneous component of the quotient algebra B/(B ∩ I_w ). We also compute the Hilbert series of this algebra. One of the main tools of this paper is a variant we found of the Robinson–Schensted–Knuth correspondence defined for single semistandard tableaux of double shape.

Robinson-Schensted-Knuth correspondence and Weak Polynomial Identities of $M_{1,1}(E)$

LA SCALA, Roberto
2005-01-01

Abstract

In this paper, it is proved that the ideal I_w of the weak polynomial identities of the superalgebra M_1,1(E) is generated by the proper polynomials [x_1, x_2, x_3] and [x_2, x_1 ][x_3, x_1 ][x_4, x_1]. This is proved for any infinite field F of characteristic different from 2. Precisely, if B is the subalgebra of the proper polynomials of F, we determine a basis and the dimension of any multihomogeneous component of the quotient algebra B/(B ∩ I_w ). We also compute the Hilbert series of this algebra. One of the main tools of this paper is a variant we found of the Robinson–Schensted–Knuth correspondence defined for single semistandard tableaux of double shape.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/9661
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact