arXiv subjects
Publications and source records attributed to Patrícia Damas Beites.
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.
The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.
It is proved that there exist no simple finite-dimensional Filippov superalgebras of type A(m,n) over an algebraically closed field of characteristic 0.
It is proved that there exist no simple finite-dimensional Filippov superalgebras of type A(0,n) over an algebraically closed field of characteristic 0.