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The algebraic and geometric classification of transposed Poisson algebras

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arxiv 2311.00459 v1 pith:HOCMHSUC submitted 2023-11-01 math.RA

classification math.RA
keywords algebraspoissontransposedalgebraicclassificationdimensionalgeometriccomplex
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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.

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  1. Compatible anti-pre-Lie algebras

    math.RA 2024-12 reject novelty 4.0 of 10

    Compatible anti-pre-Lie algebras are introduced, characterized via negative left multiplication representations, and classified in dimension 2 by a list of 45 families.

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