Finite-dimensional transposed Poisson algebras are nilpotent exactly when left multiplications are nilpotent in both associative and Lie operations, with the nilpotent radical equaling the associative radical and Frattini subalgebra contained in the derived algebra.
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Transposed Novikov-Poisson algebras are solvable iff right nilpotent iff P² is nilpotent, with these properties equivalent to those of the underlying commutative associative and Novikov algebras, and Itô's theorem holds.
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Nilpotency and Frattini theory for transposed Poisson algebras
Finite-dimensional transposed Poisson algebras are nilpotent exactly when left multiplications are nilpotent in both associative and Lie operations, with the nilpotent radical equaling the associative radical and Frattini subalgebra contained in the derived algebra.
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Solvability and nilpotency of transposed Novikov-Poisson algebras
Transposed Novikov-Poisson algebras are solvable iff right nilpotent iff P² is nilpotent, with these properties equivalent to those of the underlying commutative associative and Novikov algebras, and Itô's theorem holds.