Malcev h*-algebras.
M. Cabrera, J. Martínez Moreno, A. Rodríguez (1986)
Extracta Mathematicae
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M. Cabrera, J. Martínez Moreno, A. Rodríguez (1986)
Extracta Mathematicae
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Yury Popov (2020)
Communications in Mathematics
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We give a survey of results obtained on the class of conservative algebras and superalgebras, as well as on their important subvarieties, such as terminal algebras.
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...
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...
José Antonio Cuenca Mira (2002)
Extracta Mathematicae
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Murray R. Bremner (2014)
Commentationes Mathematicae Universitatis Carolinae
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First, we provide an introduction to the theory and algorithms for noncommutative Gröbner bases for ideals in free associative algebras. Second, we explain how to construct universal associative envelopes for nonassociative structures defined by multilinear operations. Third, we extend the work of Elgendy (2012) for nonassociative structures on the 2-dimensional simple associative triple system to the 4- and 6-dimensional systems.
Jiyuan Tao (2016)
Special Matrices
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In this paper,we state and prove an analog of Lie product formula in the setting of Euclidean Jordan algebras.
Ciobanu, Camelia (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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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,...
Angel Rodriguez Palacios (1988)
Manuscripta mathematica
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