Let G be a simple complex factorizable Poisson algebraic group. Let U (g) be the corresponding quantum group. We study the U (g)-equivariant quantization C [G] of the affine coordinate ring C[G] along the Semenov-Tian-Shansky bracket. For a simply connected group G, we give an elementary proof for the analog of the Kostant–Richardson theorem stating that C [G] is a free module over its center.

In this paper we find a certain solution of Poisson type fractional differential equation using theory tensor product Banach spaces.

in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X . If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson traces on X , i.e., distributions invariant under Hamiltonian flows. When X has finitely many symplectic leaves, we prove that M(X) is holonomic. Thus, when X ...

A change in the arrival rate of a Poisson process sometimes necessitates immediate action. If the change time is unobservable, then the design of online change detection procedures becomes important and is known as the Poisson disorder problem. Formulated and partially solved by Davis [Banach Center Publ., 1 (1976) 65–72], the standard Poisson problem addresses the tradeoff between false alarms...

Abstract: The current paper is concerned with the controllability of nonlocal secondorder impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a ne...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.