The algebraic and geometric classification of transposed δ-Poisson algebras
Annotatsiya
The algebraic and geometric classifications of complex [Formula: see text]-dimensional transposed [Formula: see text]-Poisson algebras are given. Namely, we prove that the variety of complex [Formula: see text]-dimensional transposed [Formula: see text]-Poisson algebras has dimension [Formula: see text] and seven irreducible components for [Formula: see text]; the variety of complex [Formula: see text]-dimensional transposed [Formula: see text]-Poisson algebras has dimension [Formula: see text] and five irreducible components; the variety of complex [Formula: see text]-dimensional transposed [Formula: see text]-Poisson algebras has dimension [Formula: see text] and four irreducible components; the variety of complex [Formula: see text]-dimensional transposed [Formula: see text]-Poisson algebras has dimension [Formula: see text] and five irreducible components; and the variety of complex [Formula: see text]-dimensional transposed [Formula: see text]-Poisson algebras has dimension [Formula: see text] and three irreducible components. In particular, we find the first example (in an “adequate” variety) of deformations (and degenerations) between two simple transposed anti-Poisson algebras. As a byproduct, we obtain the algebraic and geometric classification of complex [Formula: see text]-dimensional transposed scalar-Poisson algebras, i.e. algebras that are in the intersection of all varieties of transposed [Formula: see text]-Poisson algebras.