Displaying similar documents to “Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral”

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

Abanina, L., Mishchenko, S. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30 Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0. The algebras of this variety are left nilpotent of class not more than 3. We give a complete description of the vector space of multilinear identities in the language of representation theory of the symmetric group Sn and Young diagrams....

Asymptotic Behaviour of Colength of Varieties of Lie Algebras

Mishchenko, S., Zaicev, M. (2000)

Serdica Mathematical Journal

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This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128. We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics...

Commutator algebras arising from splicing operations

Sergei Sverchkov (2014)

Open Mathematics

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We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation,...

Free Bicommutative Algebras

Dzhumadil'daev, A. S., Ismailov, N. A., Tulenbaev, K. M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50. Algebras with identities a(bc)=b(ac), (ab)c=(ac)b is called bicommutative. Bases and the cocharacter sequence for free bicommutative algebras are found. It is shown that the exponent of the variety of bicommutaive algebras is equal to 2.

Operads of decorated trees and their duals

Vsevolod Yu. Gubarev, Pavel S. Kolesnikov (2014)

Commentationes Mathematicae Universitatis Carolinae

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This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction...

Characterizing Non-Matrix Properties of Varieties of Algebras in the Language of Forbidden Objects

Finogenova, Olga (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R10, 16R40. We discuss characterizations of some non-matrix properties of varieties of associative algebras in the language of forbidden objects. Properties under consideration include the Engel property, Lie nilpotency, permutativity. We formulate a few open problems. * The author acknowledges support from the Russian Foundation for Basic Research, grant 10-01-00524.