Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗ B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗A→ (S ⊗B)S⊗G is an isomorphism for any R-algebra S.

Given a simple, simply laced, complex Lie algebra g corresponding to the Lie group G, let n+ be the subalgebra generated by the positive roots. In this paper we construct a BV-algebra BV[g] whose underlying graded commutative algebra is given by the cohomology, with respect to n+, of the algebra of regular functions on G with values in ∧ (n+\g). We conjecture that BV[g] describes the algebra of...

Abstract Let G be a finite group, let A an infinite-dimensional stably simple unital C*-algebra, and $\alpha \colon \to {\operatorname {Aut}} (A)$ action of on which has the weak tracial Rokhlin property. $A^{\alpha }$ fixed point algebra. Then radius comparison satisfies ${\operatorname {rc}} (A^{\alpha }) \leq ( C^* (G, A, \alpha ) ({1}/{{{\operatorname{card}}} (G))} \cdot . The inclusion in ...

1. Lecture 1: Affine Lie algebras and the Fock representation of ĝln. 1.1. The loop algebra construction. Let g be a complex reductive Lie algebra and let L denote the algebra of Laurent polynomials in one variable L = C[t, t−1]. The loop algebra over g is L(g) = L ⊗ g, which is a Lie algebra with the bracket [t ⊗ x, t ⊗ y]0 = t[x, y]. (1.1) The elements of the loop algebra may be regarded as r...

The aim of this paper is to introduce and study Lie algebras over noncommutative rings. For any Lie algebra g sitting inside an associative algebra A and any associative algebra F we introduce and study the F -loop algebra (g, A)(F), which is the Lie subalgebra of F ⊗ A generated by F ⊗ g. In most examples A is the universal enveloping algebra of g. Our description of the loop algebra has a str...

Given an inductive limit group G = lim → Gβ , β ∈ Γ where each Gβ is locally compact, and a continuous two–cocycle ρ ∈ Z(G, T) , we construct a C*–algebra L for which the twisted discrete group algebra C∗ ρ (Gd) is imbedded in its multiplier algebra M(L) , and the representations of L are identified with the strong operator continuous ρ–representations of G . If any of these representations are...

suppose $g$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$f,$ $p=mn$ is a maximal parabolic subgroup of $g,$ $frak{n}$ is‎ ‎the lie algebra of the unipotent radical $n.$ under the adjoint‎ ‎action of its stabilizer in $m,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.

For every semi-simple Lie algebra g one can construct the DrinfeldJimbo algebra U h (g). This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U h (g), Drinfeld used the KZ-equations to construct a quasi-Hopf algebra Ag . He proved that particular categories of modules over the algebras U h (g) and Ag are tensor equivalent. Analogo...