Clifford geometric algebras, spin manifolds, and group actions in mathematics and physics (Q2655381)

This review aims to highlight the most striking features of the relationship that exists between Clifford geometric algebras, spin manifolds and group actions and to emphasize their fundamental importance for a deeper understanding the links between mathematics and such physical theories as the supergravity and superstring ones. It consists of three sections. Section 1 is largely the Introduction. Section 2 is devoted to the concept of Clifford algebra that underlies spin geometry and spinorial physics, and discusses the related topological aspects. Physical and geometrical aspects of the spinor spaces and the Dirac operator constitute the content of Section 3.