This paper demonstrates the impacts of odd and even derivations in transposed Poisson superalgebras, suggesting new frameworks for understanding super vector spaces.
Key Points
Introducing odd derivations necessitates a new super vector space concept for transposed Poisson superalgebras, expanding existing frameworks.
The study provides proof that super vector spaces generated by odd derivations comply with the compatibility requirements outlined in the new definition.
It shows that given a transposed Poisson superalgebra, one can construct a 3-Lie superalgebra through its even derivation, enriching algebraic structures.
Key operations involve a left supermodule and a Jordan bracket, shedding light on the relationships between these algebraic entities.