Journal of Lie Theory 17 (2007), No. 2, 357--377
Copyright Heldermann Verlag 2007
On Algebraic Torsion Forms and their Spin Holonomy Algebras
Niels Bernhardt
Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
niels.bernhardt@math.auckland.ac.nz
Paul-Andi Nagy
Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
nagy@math.auckland.ac.nz
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.
Keywords: Spin connection, spin holonomy algebra.
MSC: 53C10, 53C27, 53C29
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