ON THE COLENGTH OF A VARIETY OF LIE ALGEBRAS-Reference-Cited by-同舟云学术

ON THE COLENGTH OF A VARIETY OF LIE ALGEBRAS

Published:1999-10 Issue:05 Volume:09 Page:483-491
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

GIAMBRUNO A.¹,MISHCHENKO S.²,ZAICEV M.³

Affiliation:

1. Dipartimento di Matematica e Applicazioni, Università di Palermo, 90123 Palermo, Italy

2. Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk 432100, Russia

3. Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia

Abstract

We study the variety of Lie algebras defined by the identity [Formula: see text] over a field of characteristic zero. We prove that, as in the associative case, in the nth cocharacter χn of this variety, every irreducible Sn-character appears with polynomially bounded multiplicity (not greater than n2). Anyway, surprisingly enough, we also show that the colength of this variety, i.e. the total number of irreducibles appearing in χn is asymptotically equal to [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196799000291

Reference5 articles.

1. Applications of hook Young diagrams to P.I. Algebras

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