2021
DOI: 10.1016/j.geomphys.2021.104287
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The algebraic and geometric classification of nilpotent left-symmetric algebras

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Cited by 4 publications
(4 citation statements)
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“…-assosymmetric algebras [120]; -bicommutative algebras [163]; -CD-algebras [144]; -commutative algebras [89]; -left-symmetric algebras [3]; -Leibniz algebras [170]; -noncommutative Jordan algebras [128]; -Novikov algebras [137]; -right commutative algebras [4]; -right alternative algebras [121]; -terminal algebras [153]; -weakly associative algebras [9]; II. 5-dimensional nilpotent:…”
Section: The Geometric Classification Of Algebrasmentioning
confidence: 99%
“…-assosymmetric algebras [120]; -bicommutative algebras [163]; -CD-algebras [144]; -commutative algebras [89]; -left-symmetric algebras [3]; -Leibniz algebras [170]; -noncommutative Jordan algebras [128]; -Novikov algebras [137]; -right commutative algebras [4]; -right alternative algebras [121]; -terminal algebras [153]; -weakly associative algebras [9]; II. 5-dimensional nilpotent:…”
Section: The Geometric Classification Of Algebrasmentioning
confidence: 99%
“…The algebraic classification (up to isomorphism) of algebras of dimension n from a certain variety defined by a certain family of polynomial identities is a classic problem in the theory of non-associative algebras. There are many results related to the algebraic classification of small-dimensional algebras in the varieties of Jordan, Lie, Leibniz, Zinbiel, and many other algebras [2,5,6,29,38] and references in [30,36]. Geometric properties of a variety of algebras defined by a family of polynomial identities have been an object of study since 1970's (see, [5,6,13,16,21,22,28,31,33,49] and references in [30]).…”
Section: Introductionmentioning
confidence: 99%
“…There are many results related to the algebraic classification of small-dimensional algebras in the varieties of Jordan, Lie, Leibniz, Zinbiel, and many other algebras [2,5,6,29,38] and references in [30,36]. Geometric properties of a variety of algebras defined by a family of polynomial identities have been an object of study since 1970's (see, [5,6,13,16,21,22,28,31,33,49] and references in [30]). Gabriel described the irreducible components of the variety of 4-dimensional unital associative algebras [16].…”
Section: Introductionmentioning
confidence: 99%
“…Moreover, by A. Hegazi and others the analogue of Skjelbred-Sund method was presented for the Jordan and Malcev algebras [14,15]. After that in recent years central extensions method have been used to the classification of various types of nilpotent algebras, and classification of many classes of low-dimensional nilpotent algebras is obtained [1,3,6,7,16,18,20]. Moreover, all central extensions of filiform associative algebras were classified in [19], central extensions of null-filiform and some filiform Leibniz algebras were classified in [2,23], and all central extensions of filiform Zinbiel algebras were classified in [8].…”
Section: Introductionmentioning
confidence: 99%