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 ofan 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.