DENSE m-CONVEX FRÉCHET SUBALGEBRAS OF OPERATOR ALGEBRA CROSSED PRODUCTS BY LIE GROUPS

On Lie algebra crossed modules

The goal of this article is to construct a crossed module representing the cocycle 〈[, ], 〉 generating H(g; C) for a simple complex Lie algebra g.

Large Subalgebras and the Structure of Crossed Products

We give a survey of large subalgebras of crossed product C*algebras, including some recent applications (by several people), mostly to the transformation group C*-algebra C∗(Z, X, h) of a minimal homeomorphism h of a compact metric space X: • If there is a continuous surjective map from X to the Cantor set, then C∗(Z, X, h) has stable rank one (regardless of the mean dimension of h). • If there...

On crossed products of the Cuntz algebra O∞ by quasi-free actions of abelian groups

We investigate the structures of crossed products of the Cuntz algebra O∞ by quasi-free actions of abelian groups. We completely determine their ideal structures and compute the strong Connes spectra and K-groups.

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules