Transposed Poisson Superalgebras

Transposed Poisson superalgebra is a generalization of transposed Poisson algebra.In this paper,we obtain the result about transposed Poisson superalgebras,such as the closure under taking tensor products.By studying several superalgebras,we can construct new transposed Poisson superalgebra.Then we study the central extension and the universal central extension of the transposed Poisson superalgebra.Further,we also introduce the notions of Poisson 3-Lie superalgebra and transposed poisson 3-Lie superalgebra,and obtain the relation between transposed Poisson superalgebra,3-Lie superalgebra and transposed Poisson 3-Lie superalgebra.Finally,we introduce the notions of N superoperator,O superoperator and R-B superoperator on pre-Lie superalgebra,then we obtain the equivalence relation between several superoperators.