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On the exponential growth of graded Capelli polynomials

Abstract

In a free superalgebra over a field of characteristic zero we consider the graded Capelli polynomials Cap M+1[Y,X] and Cap L+1[Z,X] alternating on M+1 even variables and L+1 odd variables, respectively. Here we compute the superexponent of the variety of superalgebras determinated by Cap M+1[Y,X] and Cap L+1[Z,X]. An essential tool in our computation is the generalized-six-square theorem proved in [3].

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Correspondence to Francesca Benanti.

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Benanti, F. On the exponential growth of graded Capelli polynomials. Isr. J. Math. 196, 51–65 (2013). https://doi.org/10.1007/s11856-012-0143-8

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  • DOI: https://doi.org/10.1007/s11856-012-0143-8

Keywords

  • Characteristic Zero
  • Polynomial Identity
  • Homogeneous Degree
  • Multilinear Polynomial
  • Block Triangular Matrix