Oscillator Lie algebras are the only non commutative solvable which carry a bi-invariant Lorentzian metric. In this paper, we determine all Poisson structures, and in particular, symmetric Leibniz algebra structures whose underlying is an oscillator algebra. We give also bialgebra structure on derive some geometric consequences groups.

We study some reduced free products of C∗-algebras with amalgamations. We give sufficient conditions for the positive cone of the K0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the later result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C∗-algebras of the Baumslag-Soli...

In this paper we examine on a pair of adjoint functors (ϕ^* ,ϕ_*)for subcategory the category crossed modules over commutative algebras where ϕ_*: XMod/P → XMod/Q, induced, and ϕ^*:XMod/Q XMod/P, pullback (co-induced), which enables us to move from Q-modules P-modules by an algebra morphism ϕ : P Q. We show that functor (ϕ^*,ϕ_*) makes p∶ XMod k-Alg into bi- fibred k-Alg, algebras, p is given p...

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means the adjoint representations algebras. In this way, we calculate some four dimensional and nilpotent six symplectic real groups. Then using Magri-Morosi's theorem obtain new bi-Hamiltonian systems with as phase spaces.

Given a quasi-hereditary superalgebra A, the first author and R. Muth have defined generalized Schur bi-superalgebras TA(n) proved that these algebras are again quasi-hereditary. In particular, comes with family of standard modules. Developing work Donkin Mathieu on good filtrations, we prove tensor product modules over has filtration.

Subrahmanian 14] uses annotated logic 2] to integrate a set of deductive databases in an unique amalgamated database called amalgam. The amalgam, in addition to the disjoint union of the databases, contains a supervisory database. The supervisory database is a set of clauses (called amalgamated clauses) which resolve connicts due to inconsistent facts and compose uncertain information of diiere...

We search for pseudo-differential operators acting on holomorphic Sobolev spaces. The should mirror the standard mapping property in analogues. setting is a closed real-analytic Riemannian manifold, or Lie group with bi-invariant metric, and spaces are defined fixed Grauert tube about core manifold. find that every operator commutant of Laplacian this kind. Moreover, so all certain analytic ope...

In this paper, we show that there exist (continuum many) varieties of bi-Heyting algebras are not generated by their complete members. It follows extensions the Heyting–Brouwer logic [Formula: see text] topologically incomplete. This result provides further insight into long-standing open problem Kuznetsov yielding a negative solution reformulation from to text].