engleski

Realizations of noncommutative spaces

Most of the physics applications of noncommutative geometry are done calculating in one local system of noncommutative coordinates, i.e. a point of view is taken that the noncommutative space is described by a single noncommutative algebra. Sometimes in practice noncommutative spaces are either glued from many such pieces or appear as objects living relatively over some known space or algebra, or as deformations of known objects, or even represented solely in categorical terms. I will show several examples from my own work and collaborations, with appropriate background and context, where we need and realize spaces via noncommutative gluing, then of noncommutative relative schemes, as well as our recent realization of all Lie algebra type spaces via deformations within algebras of differential operators.

noncommutative space; localization; gluing; representation

nije evidentirano