Locally Anisotropic Supergravity and Gauge Gravity on Noncommutative Spaces

Abstract

We outline the the geometry of locally anisotropic (la) superspaces and la-supergravity. The approach is backgrounded on the method of anholonomic superframes with associated nonlinear connection structure. Following the formalism of enveloping algebras and star product calculus we propose a model of gauge la-gravity on noncommutative spaces. The corresponding Seiberg-Witten maps are established which allow the definition of dynamics for a finite number of gravitational gauge field components on noncommutative spaces.

latex2e, 14 pages, Contribution at NATO ARW ''Noncommutative Structures in Mathematics and Physics'', September 24-27, 2000, Kyiv, Ukraine