Let F < YU Z, *> be the free *-superalgebra over a field F of characteristic zero and let Gamma(M +/-, L +/-)* be the T-Z2* - ideal generated by the set. of the s-graded Capelli polynomi- als Cap(M+)((Z2,)*())[Y+, X], Cap(L+)((Z2,)*())[Z(+), X], Cap(L-)((Z2,)*())[Z-,X] alternating on M +/- symmetric variables of homogeneous degree zero, on M- skew variables of homogeneous degree zero, on L+ symmetric variables of homogeneous degree one and on L- skew variables of homogeneous degree one, respectively. We study the asymptotic behavior of the sequence of *-graded codimensions of Gamma(M)(+/-,L)(+/-)*. In particular, we prove that the s-graded codimensions of the finite dimensional simple *-superalgebras are asymptotically equal to the *-graded codimensions of Gamma(M)(+/-,L)(+/-)*, for some fixed natural numbers M+, M-, L+ and L-.

Benanti, F.S., Valenti, A. (2022). *-Graded Capelli polynomials and their asymptotics. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 32(06), 1179-1202 [10.1142/S0218196722500503].

*-Graded Capelli polynomials and their asymptotics

Benanti, FS;Valenti, A
2022-09

Abstract

Let F < YU Z, *> be the free *-superalgebra over a field F of characteristic zero and let Gamma(M +/-, L +/-)* be the T-Z2* - ideal generated by the set. of the s-graded Capelli polynomi- als Cap(M+)((Z2,)*())[Y+, X], Cap(L+)((Z2,)*())[Z(+), X], Cap(L-)((Z2,)*())[Z-,X] alternating on M +/- symmetric variables of homogeneous degree zero, on M- skew variables of homogeneous degree zero, on L+ symmetric variables of homogeneous degree one and on L- skew variables of homogeneous degree one, respectively. We study the asymptotic behavior of the sequence of *-graded codimensions of Gamma(M)(+/-,L)(+/-)*. In particular, we prove that the s-graded codimensions of the finite dimensional simple *-superalgebras are asymptotically equal to the *-graded codimensions of Gamma(M)(+/-,L)(+/-)*, for some fixed natural numbers M+, M-, L+ and L-.
Settore MAT/02 - Algebra
https://arxiv.org/abs/2111.04366
Benanti, F.S., Valenti, A. (2022). *-Graded Capelli polynomials and their asymptotics. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 32(06), 1179-1202 [10.1142/S0218196722500503].
File in questo prodotto:
File Dimensione Formato  
s0218196722500503.pdf

Solo gestori archvio

Tipologia: Versione Editoriale
Dimensione 364.92 kB
Formato Adobe PDF
364.92 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/10447/568945
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact