Speciality conjecture for transposed Poisson algebras

A transposed Poisson algebra is a commutative associative algebra equipped with a bilinear bracket satisfying the transposed Poisson identities. It is called special if it can be embedded into an appropriate Poisson algebra with derivation.

Speciality conjecture. Every transposed Poisson algebra is special.

This conjecture is motivated by the fact that Novikov commutator algebras are special, while transposed Poisson algebras form a subvariety of generalized derivation algebras and satisfy the displayed special identities. Its resolution is not given here.

Sources & referencesView supporting material

Primary source

B. K. Sartayev, “Some generalizations of the variety of transposed Poisson algebras”, arXiv:2305.12869 (2023).

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