Faculty Publications

The Reductive Pair (B3, G2) And Affine Connections On S7

Document Type

Article

Journal/Book/Conference Title

Journal of Pure and Applied Algebra

Volume

86

Issue

2

First Page

155

Last Page

171

Abstract

The reductive pair (B3, G2) over an arbitrary field F of characteristic≠2,3 is described in terms of an octonion algebra O over F and its associated spin representation. The reductive algebra associated with (B3, G2) is shown to be isomorphic to the vector Malcev algebra of O. This is applied to realize the sphere S7 as the reductive homogeneous space Spin(7)/G2 in an algebraic framework, and then to determine all invariant affine connections on S7=Spin(7)/G2 in terms of the compact Malcev algebra of dimension 7. An application is also noted in reference to Lagrangian mechanics on S7. © 1993.

Department

Department of Mathematics

Original Publication Date

5-12-1993

DOI of published version

10.1016/0022-4049(93)90100-8

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