The Algebraic and Geometric Classification of Nilpotent Right Commutative Algebras

Non-associative algebraic structures: classification and structure

“…-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:…”

The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

“…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]).…”

“…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].…”

One-generated nilpotent bicommutative algebras

“…However, this circumstance does not hold for every variety of non-associative algebras. For example, the classifications of 4-dimensional right commutative [2], assosymmetric [26], bicommutative [36], commutative [22] and terminal [32] nilpotent algebras show that there exist several one-generated algebras of dimension 4 from these varieties. Recently, one-generated nilpotent Novikov and assosymmetric algebras in dimensions 5 and 6, and one-generated nilpotent terminal algebras in dimension 5 were classified in [10,33,35].…”