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