Fredholm module

In noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial changes, the same as the abstract elliptic operator introduced by .
Definition.
If "A" is an involutive algebra over the complex numbers C, then a Fredholm module over "A" consists of 
an involutive representation of "A" on a Hilbert space "H", together with a self-adjoint operator "F", of square 1 and such that the commutator
is a compact operator, for all "a" in "A". 
References.
The paper by Atiyah is reprinted in volume 3 of his collected works, 
External link.
Fredholm module, on PlanetMath