We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R = C[X1, . . . , Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a coro...

I point out an unexpected relation between the BV (Batalin–Vilkovisky) and the BFV (Batalin–Fradkin–Vilkovisky) formulations of the same pure gauge (topological) theory. The non-minimal sector in the BV formulation of the topological theory allows one to construct the Poisson bracket and the BRST charge on some Lagrangian submanifold of the BV configuration space; this Lagrangian submanifold ca...

In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking discrete convolution with respect to space variable in system differential equations that governs its state probabilities. We call introduced as (CFPP). The explicit expression for Laplace transform probabilities are obtained whose inversion yields one-dimensional distribution. Some stati...

Let P be a Poisson algebra with Lie bracket {,} over field F of characteristic p≥0. In this paper, the structure is investigated. particular, if solvable respect to its bracket, then we prove that ideal J generated by all elements {{{x1,x2},{x3,x4}},x5} x1,…,x5∈P associative nilpotent index bounded function derived length P. We use result further and p≠2, {P,P}P nil.

A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on associative algebra which induces a bracket each representation space Rep(A,n) explicit way. In this note, we study impact changing Leibniz rules underlying bracket. This change amounts to make suitable choice A-bimodule structure A⊗A. most important cases, describe how fixes analogue Jacobi identity, and obtain indu...

Let A be the function algebra on a semisimple orbit, M , in the coadjoint representation of a simple Lie group, G, with the Lie algebra g. We study one and two parameter quantizations of A, Ah, At,h, such that the multiplication on the quantized algebra is invariant under action of the Drinfeld-Jimbo quantum group, Uh(g). In particular, the algebra At,h specializes at h = 0 to a U(g), or G, inv...

A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n − 1, where n is the dimension of space-time, Jacobi's identity is fulfilled.