Journal of Lie Theory 17 (2007), No. 4, 829--856
Copyright Heldermann Verlag 2007
Spin Holonomy Algebras of Self-Dual 4-Forms in R8
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 give a complete classification of spin holonomy algebras on eight-dimensional Euclidean spaces w.r.t. a linear spin connection constructed from a self-dual 4-form T with constant coefficients. An important role in this classification is played by the set of spinors fixed by T, which is the algebraic model for the set of parallel spinors w.r.t. the spin connection.
Keywords: Spin connection, spin holonomy algebra.
MSC: 53C10, 53C27, 53C29
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