Displaying similar documents to “Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures”

Algebras, Dialgebras, and Polynomial Identities

R. Bremner, Murray (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 17A30. Secondary 16R10, 17-08, 17A32, This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting...

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...

Malcev h*-algebras.

M. Cabrera, J. Martínez Moreno, A. Rodríguez (1986)

Extracta Mathematicae

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Some remarks on the Akivis algebras and the Pre-Lie algebras

Yuqun Chen, Yu Li (2011)

Czechoslovak Mathematical Journal

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In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I. P. Shestakov’s result that any Akivis algebra is linear and D. Segal’s result that the set of all good words in X * * forms a linear basis of the free Pre-Lie algebra PLie ( X ) generated by the set X . For completeness,...

Enveloping algebras of Malcev algebras

Murray R. Bremner, Irvin R. Hentzel, Luiz A. Peresi, Marina V. Tvalavadze, Hamid Usefi (2010)

Commentationes Mathematicae Universitatis Carolinae

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We first discuss the construction by Pérez-Izquierdo and Shestakov of universal nonassociative enveloping algebras of Malcev algebras. We then describe recent results on explicit structure constants for the universal enveloping algebras (both nonassociative and alternative) of the 4-dimensional solvable Malcev algebra and the 5-dimensional nilpotent Malcev algebra. We include a proof (due to Shestakov) that the universal alternative enveloping algebra of the real 7-dimensional simple...