Article

Transposed Poisson Structures on Schrödinger Algebra in (n+1)-Dimensional Space-Time

Yang YangSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaXiaomin TangSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaAbror KhudoyberdiyevInstitute of Mathematics, Uzbekistan Academy of Sciences, Uzbekistan

Algebra Colloquiumjournal2026en

ABI

Abstract

This paper investigates the transposed Poisson structures on the Schrödinger algebra [Formula: see text] associated with [Formula: see text]-dimensional space-time of the Schrödinger Lie group. We prove that for [Formula: see text], the algebra [Formula: see text] admits no nontrivial [Formula: see text]-derivations and, consequently, no nontrivial transposed Poisson structures. In contrast, for the case [Formula: see text], we explicitly determine all [Formula: see text]-derivations and the corresponding transposed Poisson structures on [Formula: see text]. Additionally, we demonstrate that [Formula: see text] admits a nontrivial Hom-Lie structure.

Topics

Advanced Topics in Algebra Homotopy and Cohomology in Algebraic Topology Noncommutative and Quantum Gravity Theories

Identifiers

DOI: 10.1142/s1005386726000131

Citations and references

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