Infinite-Dimensional Algebras as Extensions of Kinematic Algebras

Infinite-dimensional Lie algebras

Purely Infinite Corona Algebras and Extensions

We classify all essential extensions of the form 0 → B → D → C(X) → 0 where B is a nonunital simple separable finite real rank zero Z-stable C*algebra with continuous scale, and where X is a finite CW complex. In fact, we prove that there is a group isomorphism Ext(C(X),B) → KK(C(X),M(B)/B).

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

Dual pairs and infinite dimensional Lie algebras

We construct and study various dual pairs between finite dimensional classical Lie groups and infinite dimensional Lie algebras in some Fock representations. The infinite dimensional Lie algebras here can be either a completed infinite rank affine Lie algebra, the W1+∞ algebra or its certain Lie subalgebras. We give a formulation in the framework of vertex algebras. We also formulate several co...

Nongraded Infinite-Dimensional Simple Lie Algebras

Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article is written based on the author’s seminar talks on nongraded infinite-dimensional simple Lie algebras. The key constructional ingredients of our Lie algebras ...