Transposed Poisson structures on Galilean and solvable Lie algebras

Abstract

Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal Galilean Lie algebras do not have non-trivial $\frac{1}{2}$-derivations and as it follows they do not admit non-trivial transposed Poisson structures. Also, we proved that each complex finite-dimensional solvable Lie algebra admits a non-trivial transposed Poisson structure and a non-trivial $\mathrm{Hom}$-Lie structure.

References in corpus (14)

• On $\delta$-derivations of Lie algebras and superalgebras
• Dynamical realization of l-conformal Galilei algebra and oscillators
• Super Galilean conformal algebra in AdS/CFT
• A note on the Chevalley-Eilenberg Cohomology for the Galilei and Poincare Algebras
• Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras
• Transposed Poisson structures on Block Lie algebras and superalgebras
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• Poisson Structures on Finitary Incidence Algebras
• $\delta$-Superderivations of semisimple finite-dimensional Jordan superalgebras
• The algebraic and geometric classification of transposed Poisson algebras
• Conformal Galilei algebras, symmetric polynomials and singular vectors
• Realizations of Galilei algebras
• Generalized conformal pseudo-Galilean algebras and their Casimir operators
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra

Cited by in corpus (7)

• A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
• Transposed Poisson structures on generalized Witt algebras and Block Lie algebras
• Transposed Poisson structures
• Some generalizations of the variety of transposed Poisson algebras
• Transposed Poisson structures on the Lie algebra of upper triangular matrices
• Transposed Poisson structures on solvable and perfect Lie algebras
• Transposed Poisson structures on Lie incidence algebras