Displaying similar documents to “Embedding of dendriform algebras into Rota-Baxter algebras”

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,...

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...

Universal Enveloping Algebras of Nonassociative Structures

Tvalavadze, Marina (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99. This is a survey paper to summarize the latest results on the universal enveloping algebras of Malcev algebras, triple systems and Leibniz n-ary algebras.

q-Leibniz Algebras

Dzhumadil'daev, A. S. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25. An algebra (A,ο) is called Leibniz if aο(bοc) = (a ο b)ο c-(a ο c) ο b for all a,b,c ∈ A. We study identities for the algebras A(q) = (A,οq), where a οq b = a ο b+q b ο a is the q-commutator. Let Char K ≠ 2,3. We show that the class of q-Leibniz algebras is defined by one identity of degree 3 if q2 ≠ 1, q ≠−2, by two identities of degree 3 if q = −2, and by the commutativity identity and one identity...

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.

The class of 2-dimensional neat reducts is not elementary

Tarek Sayed Ahmed (2002)

Fundamenta Mathematicae

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SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends...