On algebraic torsion forms and their spin holonomy algebras

Details On algebraic torsion forms and their spin holonomy algebras On algebraic torsion forms and their spin holonomy algebras

2006-08-21

arxiv.org/abs/math/0608509v1

Mathematics

Differential Geometry

30 pages

Scientific paper

We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish general properties of the holonomy algebras under some mild conditions on the generating element. We show that the first non-standard situation to look at appears in dimension 8 and concerns self-dual 4-forms. In this case complete structure results are obtained.

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