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Hochschild cohomologies and deformations of the pointwise superproduct

“…As in [15] and [16], we set f (z) = e zp and g(z) = e zk in some neighborhood of the point x. By (4.1), 1 Let z = (x, ξ).…”

Cohomology of the Poisson Superalgebra on Spaces of Superdimension (2, n −)

“…, τ(k s )). 2 We define P p1,p2,...,ps , filtration of polynomials by the lowest degree. 2 To avoid misunderstanding, we recall that k i are supervariables; hence, the polynomials that we call symmetric are not necessarily symmetric in the usual sense with respect to the components of the supervariables.…”

“…Therefore, to solve Eq. (4.1), we use the method proposed in [2]. Let x ∈ U , where U ∈ R 2 is a bounded domain.…”

“…The lower cohomology spaces (up to the second) of the Poisson algebra of smooth complex-valued functions on R n were found in [2]. Deformations of the Lie superalgebra of Hamiltonian vector fields with polynomial coefficients were studied in [3].…”

Deformations of the nondegenerate constant Poisson bracket and antibracket on superspaces of an arbitrary superdimension

“…The purely Grassmannian case was considered in [6]. The bosonic Poisson algebra realized on smooth functions was considered in [7]. The result depends on the chosen function space (see [5] for more details).…”