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 .
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.