Proceedings of the Japan Academy, Series A, Mathematical Sciences

Exterior differential algebras and flat connections on Weyl groups

Anatol N. Kirillov and 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 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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 2 (2005), 30-35.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116442057

Digital Object Identifier
doi:10.3792/pjaa.81.30

Mathematical Reviews number (MathSciNet)
MR2126074

Zentralblatt MATH identifier
1101.58006

Subjects
Primary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]
Secondary: 16W30

Keywords
Noncommutative differential calculus Weyl groups

Citation

Kirillov, Anatol N.; Maeno, Toshiaki. Exterior differential algebras and flat connections on Weyl groups. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 2, 30--35. doi:10.3792/pjaa.81.30. https://projecteuclid.org/euclid.pja/1116442057


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References

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