The algebraic and geometric classification of transposed Poisson algebras

Abstract

The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.

arXiv admin note: text overlap with arXiv:2207.00281

References in corpus (7)

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• Transposed Poisson structures
• The algebraic and geometric classification of Zinbiel algebras
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• On the Kantor product, II
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Cited by in corpus (9)

• Transposed Poisson structures on Galilean and solvable Lie algebras
• A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
• Transposed Poisson structures on generalized Witt algebras and Block Lie algebras
• Transposed Poisson structures
• Some generalizations of the variety of transposed Poisson algebras
• Transposed Poisson structures on the Lie algebra of upper triangular matrices
• Transposed Poisson structures on solvable and perfect Lie algebras
• Transposed Poisson structures on Lie incidence algebras
• The algebraic classification of nilpotent Novikov algebras