The Noncommutative Phase Space: An Algebraic Approach to Differential Geometry

Abstract

In this thesis we will study the phase space, Ph(A), for an associative k-algebra A. The phase space can be considered as a noncommutative tangent bundle. We will derive algebraic notions of points, curves, tangent vectors and vector fields, in addition to study differentiation of vector fields, and look at what are called integrable distributions.