Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 377-395 (2005)

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Spin groups over a commutative ring and the associated root data (odd rank case)

Hisatoshi Ikai

Mathematical Institute, Tohoku University, Sendai 980-8578, Japan e-mail:

Abstract: Spin and Clifford groups as group schemes of semi-regular quadratic spaces of odd rank over a commutative ring are shown to be smooth and reductive. Analogously to the hyperbolic case smooth open neighborhoods of unit sections, called big cells, are constructed and examined. Jordan pairs again play a role through an imbedding into hyperbolic space whose rank is higher by one. The property reductive is now proved by constructing maximal tori and their associated root data explicitly.

Keywords: Spin groups, jordan pairs, root data

Classification (MSC2000): 14L15; 17C30

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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.

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