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- Title
Analyzing the Weyl Construction for Dynamical Cartan Subalgebras.
- Authors
Duwenig, Anna; Gillaspy, Elizabeth; Norton, Rachael
- Abstract
When the reduced twisted -algebra of a non-principal groupoid admits a Cartan subalgebra, Renault's work on Cartan subalgebras implies the existence of another groupoid description of. In an earlier paper, joint with Reznikoff and Wright, we identified situations where such a Cartan subalgebra arises from a subgroupoid of. In this paper, we study the relationship between the original groupoids and the Weyl groupoid and twist associated to the Cartan pair. We first identify the spectrum of the Cartan subalgebra. We then show that the quotient groupoid acts on , and that the corresponding action groupoid is exactly the Weyl groupoid of the Cartan pair. Lastly, we show that if the quotient map admits a continuous section, then the Weyl twist is also given by an explicit continuous -cocycle on.
- Subjects
RENAULT SA; COCYCLES; GROUPOIDS
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 20, p15721
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnab114