Transposed Poisson structures on solvable and perfect Lie algebras
Ivan Kaygorodov,
Abror Khudoyberdiyev
Abstract:We described all transposed Poisson algebra structures on 
oscillator Lie algebras, i.e., on one-dimensional 
solvable extensions of the $(2n+1)$-dimensional Heisenberg algebra; 
 on solvable Lie algebras with naturally graded filiform
nilpotent radical;
 on $(n+1)$-dimensional solvable extensions of the $(2n+1)$-dimensional Heisenberg algebra; 
 and on $n$-dimensional solvable extensions of the $n$-dimensional algebra with trivial multiplication.
… Show more
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is given.
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is given.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.