On the Kantor product, II

Abstract

We describe the Kantor square (and Kantor product) of multiplications, extending the classification proposed in [I. Kaygorodov, On the Kantor product, Journal of Algebra and Its Applications, 16 (2017), 9, 1750167]. Besides, we explicitly describe the Kantor square of some low dimensional algebras and give constructive methods for obtaining new transposed Poisson algebras and Poisson-Novikov algebras; and for classifying Poisson structures and commutative post-Lie structures on a given algebra.

References in corpus (8)

• Degenerations of Leibniz and anticommutative algebras
• Special and exceptional mock-Lie algebras
• Degenerations of Jordan Algebras and ''Marginal'' Algebras
• Conservative algebras of 2-dimensional algebras
• Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
• On anticommutative algebras for which $[R_a,R_b]$ is a derivation
• On certain classes of algebras in which centralizers are ideals
• Commutative Post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras

Cited by in corpus (3)

• The algebraic and geometric classification of transposed Poisson algebras
• Transposed Poisson structures
• Conservative algebras of $2$-dimensional algebras, IV