Abstract We prove that every Novikov–Poisson algebra over a field of zero characteristic can be embedded into commutative conformal with derivation. As corollary, we show commutator Gelfand–Dorfman obtained from is special, i.e., embeddable differential Poisson algebra.

Let X be a complex elliptic curve. In this paper we define a natural Poisson structure on the moduli spaces of stable triples (E1, E2,Φ) where E1, E2 are algebraic vector bundles on X of fixed ranks (r1, r2) and degrees (d1, d2), Φ : E2 → E1 is a homomorphism. Such triples are considered up to an isomorphism and the stability condition depends on a real parameter τ . These moduli spaces were in...

Let us assume that (S,S) is a metric space with Borel σ algebra S and η̃ is a time homogeneous compensated Poisson random measure defined on a filtered probability space (Ω;F ; (Ft)0≤t<∞;P) with intensity measure ν on S, to be specified later. Let us assume that 1 < p ≤ 2, E is a Banach space of martingale type p, see e.g. the Appendix of [7] for a definition. We consider in the following the It...

Poisson algebras are usually defined as structures with two operations, a commutative associative one and an anti-commutative one that satisfies the Jacobi identity. These operations are tied up by a distributive law, the Leibniz rule. We present Poisson algebras as algebras with one operation, which enables us to study them as part of non-associative algebras. We study the algebraic and cohomo...

The structure of Poisson polynomial algebras of the type obtained as semiclas-sical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only finitely many Poisson prime ideals invariant are obtained. Combined with previous work of the first-named author, this establishes the Poisson Dixmier-Moeglin equi...

In this paper, first, we introduce the new concept of 2-inner product on Banach modules over a $C^*$-algebra. Next,  we present the concept of 2-linear operators over a $C^*$-algebra. Our result improve  the main result of the paper  Z. Lewandowska.  In the final of this paper, we define the notions 2-adjointable mappings between 2-pre Hilbert C*-modules and prove supperstability of them ...

Let us assume that (S,S) is a metric space with Borel σ algebra S and η̃ is a time homogeneous compensated Poisson randommeasure defined on a filtered probability space (Ω;F ; (Ft)0≤t<∞;P) with intensity measure ν on S, to be specified later. Let us assume that 1 < p ≤ 2, E is a Banach space of martingale type p, see e.g. the Appendix of [7] for a definition. We consider in the following the Itô...

Let G be a simple complex algebraic group equipped with a factorizable Poisson Lie structure. Let U~(g) be the corresponding quantum group. We study U~(g)-equivariant quantization C~[G] of the affine coordinate ring C[G] along the Semenov-Tian-Shansky Poisson Lie bracket. For a simply connected group G we prove an analog of the KostantRichardson theorem stating that C~[G] is a free module over ...

‎let $x$‎, ‎$y$ and $z$ be banach spaces and $f:xtimes y‎ ‎longrightarrow z$ a bounded bilinear map‎. ‎in this paper we‎ ‎study the relation between arens regularity of $f$ and the‎ ‎reflexivity of $y$‎. ‎we also give some conditions under which the‎ ‎arens regularity of a banach algebra $a$ implies the arens‎ ‎regularity of certain banach right module action of $a$‎ .