Degenerate Spin Groups as Semi-Direct Products

Dereli T., Kocak S., LİMONCU M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.20, no.3-4, pp.565-573, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 3-4
  • Publication Date: 2010
  • Doi Number: 10.1007/s00006-010-0210-3
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.565-573
  • Keywords: Degenerate Spin Groups, Clifford algebras
  • Anadolu University Affiliated: Yes

Abstract

Let Q be a symmetric bilinear form on R(n)=R(p+q+r) with corank r, rank p+q and signature type (p, q), p resp. q denoting positive resp. negative dimensions. We consider the degenerate spin group Spin(Q) = Spin(p, q, r) in the sense of Crumeyrolle and prove that this group is isomorphic to the semi-direct product of the nondegenerate and indefinite spin group Spin(p, q) with the additive matrix group Mat (p + q, r)