The Journal of the Indian Mathematical Society

Hisatoshi Ikai ¹

Affiliations
1 Aramaki-aza-aoba 400-A-101, Sendai 980-0845, JP

Abstract

An explicit formula is proved for Cayley-Lipschitz transformations, which reinforces the relation known earlier between these transformations and big cells of orthogonal and Clifford groups. In the course of proof, certain quasi-inverses are calculated generically for Jordan pairs of alternating two-tensors.

Keywords

Cayley–Lipschitz Transformations, Orthogonal and Clifford Groups Over Rings, Quasi-Inverses.

Full Text

     

Hisatoshi Ikai ¹

Affiliations
1 Mathematical Institute, Tohoku University, Sendai 980-8578, JP

Abstract

Cayley’s rational parameterization of orthogonal groups (Cayley transform) and its lifting to coverings discovered by Lipschitz are generalized. They acquire validity with functorial behavior for all regular and semirefular quadratic modules over any commutative base ring. Exterior algebras and their exponential maps play fundamental role.

Full Text