This paper investigates the transposed Poisson structures on the Schrödinger algebra S_(n)associated with(n+1)-dimensional space-time of the Schrödinger Lie group.We prove that for n≠2,the algebra S_(n)admi...This paper investigates the transposed Poisson structures on the Schrödinger algebra S_(n)associated with(n+1)-dimensional space-time of the Schrödinger Lie group.We prove that for n≠2,the algebra S_(n)admits no nontrivial 12-derivations and,consequently,no nontrivial transposed Poisson structures.In contrast,for the case n=2,we explicitly determine all 1/2-derivations and the corresponding transposed Poisson structures on S_(2).Additionally,we demonstrate that S_(2)admits a nontrivial Hom-Lie structure.展开更多
基金supported in part by National Natural Science Foundation of China(No.12271085)Natural Science Foundation of Heilongjiang Province(No.PL2024A007)Basic Scientific Research Expenses of Colleges and Universities in Heilongjiang Province(No.2023-KYYWF-1450).
文摘This paper investigates the transposed Poisson structures on the Schrödinger algebra S_(n)associated with(n+1)-dimensional space-time of the Schrödinger Lie group.We prove that for n≠2,the algebra S_(n)admits no nontrivial 12-derivations and,consequently,no nontrivial transposed Poisson structures.In contrast,for the case n=2,we explicitly determine all 1/2-derivations and the corresponding transposed Poisson structures on S_(2).Additionally,we demonstrate that S_(2)admits a nontrivial Hom-Lie structure.
