Let L be a completely valued nonarchimedean field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) agrees with its Arens-Michael envelope and, furthermore, is a stably flat completion of its universal enveloping algebra. As an application, we prove that the Taylor relative cohomology for the locally convex algebra F(g) is naturally isomorphic to the L...

Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

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a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

In a recent work [FR], Frenkel and Reshetikhin developed the theory of q-vertex operators. They showed that n-point correlation functions associated to q-vertex operators satisfy a qdifference equation called q-deformed Kniznik-Zamolodchikov equation. In the derivation of this equation, a crucial point is that the quantum affine algebra is a quasi-triangular Hopf algebra. By using several prope...

In this note we prove, for groups G fulfilling the Atiyah conjecture, a lemma relating arbitrary G-modules to free group-von-Neumann-algebra modules. As an immediate application we get properties of finitely generated pro-jective G-modules and G-modules. Other related arguments are envisaged. G; it can be defined as algebra of all (left) G-equivariant bounded linear operators on the Hilbert spa...

This study used a case to map teaching practice supervisors' experiences of being involved in developing the mobile app (TPMA) for supervising students at an open distance e-learning (ODeL) institution. The technology acceptance model (TAM) was as theoretical framework study. Data were collected through semi structured interviews and analyzed thematically. perceived usefulness participating dev...

Recently, motivated by supersymmetric gauge theory, Cachazo, Douglas, Seiberg, and Witten proposed a conjecture about finite dimensional simple Lie algebras, and checked it in the classical cases. We prove the conjecture for type G2, and also verify a consequence of the conjecture in the general case. 1. The CDSW conjecture Let g be a simple finite dimensional Lie algebra over C. We fix an inva...