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Connections on Cahen-Wallach Spaces

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Abstract

We systematically discuss connections on the spinor bundle of Cahen-Wallach symmetric spaces. A large class of these connections is closely connected to a quadratic relation on Clifford algebras. This relation in turn is associated to the symmetric linear map that defines the underlying space. We present various solutions of this relation. Moreover, we show that the solutions we present here provide a complete list with respect to a particular algebraic condition on the parameters that enter into the construction.

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  1. Faculty of Mathematics, TU Dortmund University, 44221, Dortmund, Germany

    Frank Klinker

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  1. Frank Klinker
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Correspondence to Frank Klinker.

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Klinker, F. Connections on Cahen-Wallach Spaces. Adv. Appl. Clifford Algebras 24, 737–768 (2014). https://doi.org/10.1007/s00006-014-0451-7

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  • DOI: https://doi.org/10.1007/s00006-014-0451-7

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