Lie Algebras, Vertex

Operator Algebras, and Related Topics

The historical developments and more recent advances of the theory of partial actions in

operator algebras and dynamical systems are explained in Exel's book [42].

The results will have a lasting impact on and connect further the theories of non-commutative geometry,

operator algebras, Lie theory, quantum group theory and partly quantum physics.

Vertex

operator algebras with central charge 1/2 and -68/7 .

He presents the theory of Krichever-Nobikov algebras, Lax

operator algebras, their interaction, elements of their representation theory, relations to moduli spaces of Riemann surface and holomorphic vector bundles of them and to Lax integrable systems and conformal field theory.

Other topics of the 17 papers include nonself-adjoint

operator algebras for dynamical systems, noncommutative geometry as a functor, examples of mases in C*-algebras, simple group graded rings, and classifying monotone complete algebras of operators.

This time it was decided to expand the scope by including some further topics related to interpolation, such as inequalities, invariant theory, symmetric spaces,

operator algebras, multilinear algebra and division algebras, operator monotonicity and convexity, functional spaces and applications and connections of these topics to nonlinear partial differential equations, geometry, mathematical physics, and economics.

Characterizing linear maps on

operator algebras is one of the most active and fertile research topics in the theory of

operator algebras during the past one hundred years.

Fillmore, A User's guide to

operator algebras, Willey-Interscience, 1996.

Ringrose, Fundamentals of the Theory of

Operator Algebras, Elementary Theory, New York, 1983.

One of the first applications of these ideas to

operator algebras was the realization that nuclearity for C*-algebras is equivalent to the completely positive approximation property (see [4,16,18]).

He made a connection between

operator algebras and knot theory," says Birman, whose work on "braids" provided an important link.