| 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 some series of examples in arbitrary dimensions and prove some 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 $4$-forms. In this case complete structure results are obtained when moreover assuming the $4$-form to be self-dual. |
Keywords
connection with torsion, holonomy algebra
Math Review Classification
Primary 53C10, 53C27, 53C29
Last Updated
10.08.06
Length
30 pages
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