Noncommutative

Some articles on noncommutative:

Noncommutative Quantum Field Theory - History and Motivation
... mathematicians, most notably Alain Connes, developed noncommutative geometry ... things, this work generalized the notion of differential structure to a noncommutative setting ... led to an operator algebraic description of noncommutative space-times, and the development of a Yang-Mills theory on a noncommutative torus ...
JLO Cocycle
... In noncommutative geometry, the JLO cocycle is a cocycle (and thus defines a cohomology class) in entire cyclic cohomology ... In noncommutative geometry, the concept of a manifold is replaced by a noncommutative algebra of "functions" on the putative noncommutative space ... information about the topology of that noncommutative space, very much as the deRham cohomology contains the information about the topology of a conventional manifold ...
ADHM Construction - Generalizations - Noncommutative Instantons
... In a noncommutative gauge theory, the ADHM construction is identical but the moment map is set equal to the self-dual projection of the noncommutativity ... The noncommutative instantons were discovered by Nikita Nekrasov and Albert Schwarz in 1998 ...
Skew Lattice - Historical Background
... For over 60 years, noncommutative variations of lattices have been studied with differing motivations ... of lattice theory for others it was a search for noncommutative forms of logic and Boolean algebra and for others it has been the behavior of idempotents in rings ... A noncommutative lattice, generally speaking, is an algebra where and are associative, idempotent binary operations connected by absorption identities ...
H-vector - Flag h-vector and cd-index
... of its order complex Δ(P) The flag h-vector of P can be displayed via a polynomial in noncommutative variables a and b ... define the corresponding monomial in a and b, Then the noncommutative generating function for the flag h-vector of P is defined by From the relation between αP(S) and βP(S ... Fine noted an elegant way to state these relations there exists a noncommutative polynomial ΦP(c,d), called the cd-index of P, such that Stanley proved that all coefficients of ...