Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from affine super Yangian [Formula: see text] to universal enveloping algebra of rectangular W-superalgebra for all m ≠ n, m, n ≥ 2 or 3, = 0. Furthermore, show that image this is dense, provided k + ( − n)( l 1)

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

The algebra Ψ(M) of order zero pseudodifferential operators on a compact manifold M defines a well-known C∗-extension of the algebra C(S∗M) of continuous functions on the cospherical bundle S∗M ⊂ T ∗M by the algebra K of compact operators. In his proof of the index theorem, Higson defined and used an asymptotic homomorphism T from C0(T ∗M) to K, which plays the role of a deformation for the com...

Let G be a connected reductive group acting on a finite dimensional vector space V . Assume that V is equipped with a G-invariant symplectic form. Then the ring O(V ) of polynomial functions becomes a Poisson algebra. The ring O(V ) of invariants is a sub-Poisson algebra. We call V multiplicity free if O(V ) is Poisson commutative, i.e., if {f, g} = 0 for all invariants f and g. Alternatively, ...

and [[xy]z] + [[yz]x] + [[zx]y] = 0. Left multiplication in a Lie algebra is denoted by ad(x): ad(x)(y) = [x, y]. An associative algebra A becomes a Lie algebra A− under the product, [xy] = xy − yx. The first axiom implies that [xy] = −[yx] and the second (called the Jacobi identity) implies that x 7→ adx is a homomorphism of L into the Lie algebra (EndL)−, that is, ad [xy] = [adx, ad y]. Assum...

As a continuation of [7], we introduce the notions of topological subalgebras, topological ideals and topological homomorphisms in topological BCI-algebras and study some related properties. In the section 3, we investigate the compactness in a TBCI-algebra X and quotient TBCI-algebra X=I where I is a topological ideal of X. In the section 4, we introduce the notion of topological homomorphisms...

We consider Nambu-Poisson 3-algebras on three dimensional manifolds M3, such as the Euclidean 3-space R, the 3-sphere S as well as the 3-torus T . We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms SDiff(M3) is identical to the Nambu-Poisson algebra on M3. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation...

Let P be a Poisson homogeneous G-space. In [Dr2], Drinfeld shows that corresponding to each p ∈ P , there is a maximal isotropic Lie subalgebra lp of the Lie algebra d, the double Lie algebra of the tangent Lie bialgebra (g, g∗) of G. Moreover, for g ∈ G, the two Lie algebras lp and lgp are related by lgp = Adg lp via the Adjoint action of G on d. In particular, they are isomorphic as Lie algeb...