
Journal of Lie Theory 17 (2007), No. 4, 829856 Copyright Heldermann Verlag 2007 Spin Holonomy Algebras of SelfDual 4Forms in R^{8} Niels Bernhardt Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand niels.bernhardt@math.auckland.ac.nz PaulAndi 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 eightdimensional Euclidean spaces w.r.t. a linear spin connection constructed from a selfdual 4form 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 [ Fulltextpdf (264 KB)] for subscribers only. 