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Exterior differential algebras and flat connections on Weyl groups

Anatol N. Kirillov·Toshiaki Maeno
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Abstract

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat connections in the left-invariant exterior differential algebra of $W.$ For root systems of type $A$ and $D$ we describe a set of relations between the flat connections, which conjecturally is a complete set.

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Anatol N. Kirillov, Toshiaki Maeno. 2004-07-20. Exterior differential algebras and flat connections on Weyl groups. https://arxiv.org/abs/math/0407291

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