Let *3* be the algebra of polynomials in one indeterminate x over the complex field C. Suppose || • || is a norm on 9 such that the coefficient functionals c,: X a.oc' —* a, (j = 0,1,2, • • •) are all continuous with respect to || • ||, and let K CC be the set of characters on 9> which are || • ||-continuous. Then K is compact, C\K is connected, and 0 G K. Let A be the completion of 9 with resp...

Let F be an affine flat group scheme over a commutative ring R, and S an F -algebra (an R-algebra on which F acts). We define an equivariant analogue QF (S) of the total ring of fractions Q(S) of S. It is the largest F -algebra T such that S ⊂ T ⊂ Q(S), and S is an F -subalgebra of T . We study some basic properties. Utilizing this machinery, we give some new criteria for factoriality (UFD prop...

We provide a necessary and sufficient condition for type D Temperley-Lieb algebra TLDn(δ) being semi-simple by studying branching rule cell modules. As byproduct, our result is used to study the so-called forked algebra, which quotient of TLDn(δ).

In this article, we generalize Loday and Pirashvili's [11] computation of the Ext-category Leibniz bimodules for a simple Lie algebra to case (non Lie) algebra. Most arguments easily, while main new ingredient is Feldvoss-Wagemann's cohomology vanishing theorem semi-simple algebras.

Associated to every subset J of nodes of a Dynkin diagram is a standard parabolic subalgebra pJ of the corresponding Lie algebra g, generated by the positive Borel subalgebra of g together with the negative simple generators fj, j ∈ J . Furthermore one has a decomposition of g as a semi-direct product of pJ and the subalgebra n − J generated by the remaining negative simple generators. In the s...

It is well-known that principal chiral models and symmetric space models in two-dimensional Minkowski space have an infinite-dimensional algebra of hidden symmetries. Because of the relevance of symmetric space models to duality symmetries in string theory, the hidden symmetries of these models are explored in some detail. The string theory application requires including coupling to gravity, su...

Differential calculi of Poincaré-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of PoincaréBirkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gln, Abelian Lie algebras, the...

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...

Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...