Abstract
Let A be a finite-dimensional associative algebra over a field of characteristic 0. Then there exist C ∈ ℚ+ and t ∈ ℤ+ such that gc n (A) ∼ Cn t d n as n → ∞, where d = PIexp(A). In particular, Amitsur’s and Regev’s conjectures hold for the codimensions gc n (A) of generalized polynomial identities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. I. Beidar, W. S. Martindale, and A. V. Mikhalev, Rings with Generalized Polynomial Identities, Marcel Dekker, New York (1996).
A. Berele and A. Regev, “Asymptotic behavior of codimensions of p.i. algebras satisfying Capelli identities,” Trans. Am. Math. Soc., 360, 5155–5172 (2008).
V. S. Drensky, “Relations for the cocharacter sequences of T-ideals,” in: Algebra, Proc. Int. Conf. Memory A. I. Mal’cev, Novosibirsk/USSR 1989, Pt. 2, Contemp. Math., Vol. 131, Amer. Math. Soc., Providence (1992), pp. 285–300.
A. S. Gordienko, “Regev’s conjecture and cocharacters of associative algebras of p.i. exponent 1 and 2,” Mat. Zametki, 83, No. 6, 815–824 (2008).
A. Regev, “Codimensions and trace codimensions of matrices are asymptotically equal,” Israel J. Math., 48, No. 2-3, 246–250 (1984).
M. V. Zaicev and A. Giambruno, Polynomial Identities and Asymptotic Methods, Math. Surveys Monographs, Vol. 122, Amer. Math. Soc., Providence (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 7, pp. 53–62, 200.
Rights and permissions
About this article
Cite this article
Gordienko, A.S. Regev’s and Amitsur’s conjectures for codimensions of generalized polynomial identities. J Math Sci 164, 188–194 (2010). https://doi.org/10.1007/s10958-009-9719-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-009-9719-1