We introduce a dual notion of the Poisson algebra, called the transposed Poisson algebra,
by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson …

The algebraic and geometric classification of transposed Poisson algebras | Revista de la Real
Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Skip to main content …

arXiv:2306.00425v2 [math.RA] 1 Nov 2023 Page 1 Communications in Mathematics 32 (2024),
no. 3, 1–62 DOI: https://doi.org/10.46298/cm.11419 ©2024 Ivan Kaygorodov This is an open …

Transposed Poisson Structures | Results in Mathematics Skip to main content SpringerLink
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Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras
are described. It is proven that all principal Galilean Lie algebras do not have non-trivial 1 2 …

Abstract We describe 1 2-derivations, and hence transposed Poisson algebra structures, on
Witt type Lie algebras V (f), where f: Γ→ C is non-trivial and f (0)= 0. More precisely, if| f (Γ)|≥ …

The approach for Poisson bialgebras characterized by Manin triples with respect to the
invariant bilinear forms on both the commutative associative algebras and the Lie algebras …

In the present paper, we introduce the notion of a δ-biderivation. First, we provide some
properties of δ-biderivations and illustrate their applications. In particular, we establish a …

We describe transposed Poisson algebra structures on Block Lie algebras B (q) and Block
Lie superalgebras S (q), where q is an arbitrary complex number. Specifically, we show that …

We describe transposed Poisson structures on generalized Witt algebras W (A, V,⟨·,·⟩) and
Block Lie algebras L (A, g, f) over a field F of characteristic zero, where⟨·,·⟩ and f are non …