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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E. Aljadeff, A. Giambruno and D. La Mattina, Graded polynomial identities and exponential growth, Journal für die Reine und Angewandte Mathematik 650 (2011), 83–100.
F. Benanti, A. Giambruno and M. Pipitone, Polynomial identities on superalgebras and exponential growth, Journal of Algebra 269 (2003), 422–438.
P. B. Cohen and A. Regev, A six generalized squares theorem, with application to polynomial identity algebras, Journal of Algebra 239 (2001), 174–190.
A. Giambruno and D. La Mattina, Graded polynomial identities and codimensions: computing the exponential growth, Advances in Mathematics 259 (2010), 859–881.
A. Giambruno and A. Regev, Wreath products and P.I. algebras, Journal of Pure and Applied Algebra 35 (1985), 133–149.
A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, Vol 122, American Mathematical Society, Providence, RI, 2005.
A. R. Kemer, Ideal of Identities of Associative Algebras, Translations of Mathematical Monographs, Vol. 87, American Mathematical Society, Providence, RI, 1991.
S. P. Mishchenko, A. Regev and M. Zaicev, The exponential growth of codimension for Capelli identities, Israel Journal of Mathematics 115 (2000), 333–342.
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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