where G is a finite group. If we want to understand the differential geometry behind the DW-model we have to give up the finiteness of G of course. If G is a Lie group, we can ask ourselves what geometric objects correspond to smooth homomorphisms from π1(M) to G (we will not explain here what we mean by smoothness exactly). The answer is well known: principal Gbundles with flat connections. We...

OF THE DISSERTATION Global Weyl Modules for Twisted and Untwisted Loop Algebras by Nathaniael Jared Manning Doctor of Philosophy, Graduate Program in Mathematics University of California, Riverside, June 2012 Dr. Vyjayanthi Chari, Chairperson A family of modules called global Weyl modules were defined in [7] over algebras of the form g⊗A, where g is a simple finite–dimensional complex Lie algeb...

We prove that, if A and B are complete normed non-associative algebras, and if B is strongly semisimple and algebraic, then dense range homomorphisms from A to B are continuous. As a consequence, we obtain that homomorphisms from complete normed algebras into a complete normed power-associative algebraic algebra B are continuous if and only if B has no nonzero elements with zero square. We also...

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...

Let $\mathcal A$ be a unital $C^*$-algebra. We consider Jordan $*$-homomorphisms on $C(X, \mathcal A)$ and Lip$(X,\mathcal A)$. More precisely, for any $C^*$-algebra A$, we prove that every $*$-homomorph

We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular W-algebras both in type A. The construction is given via coproduct and evaluation map for Yangians. As a consequence, we show that parabolic inductions representations can be regarded as tensor product under homomorphisms. same method applicable also super-setting.