Non-Commutative Analysis
Kalyan B. Sinha
In non-commutative analysis,
the traditional (commutative) algebras of
functions on manifolds are replaced
by non-commutative algebras such as
von Neumann algebras and C* algebras.
Originating in quantum physics,
non-commutative analysis has grown
extensively in recent years, especially
through the works of Connes in
non-commutative geometry. Just as
the Laplacian and Dirac operators can
be used to study the geometry of
manifolds, non-commutative analogs
of the Dirac operator can be used
to study geometric characteristics
on non-commutative manifolds such as
the quantum Heisenberg group. This
talk will give an overview of concepts,
as well as results and examples in
non-commutative analysis.
1