2002/12/31 by Ricardo A. Mosna, David Miralles, Jayme Vaz +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #math-ph #math.MP #msc:15A66 #msc:15A75 #msc:16W55 #msc:81R05
paper · pdf · doi:10.1088/0305-4470/36/15/312
published as J. Phys. A 36, 4395-4405 (2003) · 10 pages, LaTeX; v2 accepted for publication in J. Phys. A
arxiv created 2003/03/12 · openalex publication_date 2003/04/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Let ℓ( V , g ) be the real Clifford algebra associated with the real vector space V , endowed with a nondegenerate metric g . In this paper, we study the class of 2 -gradings of ℓ( V , g ) which are somehow compatible with the multivector structure of the Grassmann algebra over V . A complete characterization for such 2 -gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of ℓ( V , g ) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on ℓ( V , g ) by 2 -gradings of this algebra.