We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q → 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed point subalgebra of the loop algebra glN [λ, λ −1] with respect to a natural involution corresponding to the embedding of the orthogonal or symplectic Lie algeb...

In this paper, we describe linear maps between complex Banach algebras that preserve products equal to fixed elements. This generalizes some important special cases where the elements are zero or identity element. First show if such map preserves a finite-rank operator, then it must also product. several instances, is enough product preserving be scalar multiple of an algebra homomorphism. Seco...

Let B be a stable continuous trace C*-algebra with spectrum Y . We prove that the natural suspension map S, : [Co(X), B ] -+ [Co(X)@ Co(R), B @ Co(R)] is a bijection, provided that both X and Y are locally compact connected spaces whose one-point compactifications have the homotopy type of a finite CW-complex and X is noncompact. This is used to compute the second homotopy group of 9 in terms o...

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties. 1 A precise version of the localization theorem Let X be a topological space with...

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphi...

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

The momentum map is essentially due to Lie, [5], pp. 300–343. The modern notion is due to Kostant [3], Souriau [9], and Kirillov [2]. The setting for the moment mapping is a smooth symplectic manifold (M,ω) or even a Poisson manifold (M,P ) with the Poisson bracket on functions {f, g} = P (df, dg) (where P = ω : T M → TM is the Poisson tensor). To each function f there is the associated Hamilto...