Clifford geometric algebras, spin manifolds, and group actions in mathematics and physics
type: Item
instance of: scholarly article
title: Clifford geometric algebras, spin manifolds, and group actions in mathematics and physics
zbMATH Open document ID: 1194.00067
author: Luciano Boi
published in: Advances in Applied Clifford Algebras
publication date: 2010-01-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 00A79
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 83C60
Mathematics Subject Classification ID: 11E57
Mathematics Subject Classification ID: 11E39
zbMATH DE Number: 5662204
zbMATH Keywords: Clifford geometric algebras
zbMATH Keywords: Clifford bundle
zbMATH Keywords: spin group
zbMATH Keywords: complex manifolds
zbMATH Keywords: spinors
zbMATH Keywords: Dirac operator
zbMATH Keywords: curvature and topology
zbMATH Keywords: mathematical physics
zbMATH Keywords: strings and symmetries
zbMATH Keywords: group actions
zbMATH Keywords: Hopf gomotopy groups
zbMATH Keywords: Bott periodicity theorem
zbMATH Keywords: Atiyah-Singer index theorem
reviewed by: Eugene Kryachko
MaRDI profile type: Publication
full work available at URL: s00006-009-0199-7
OpenAlex ID: W2065061845
DOI: 10.1007/S00006-009-0199-7
description: scientific article