Fourier transforms and Ringel–Hall algebras of valued quivers
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- by Chenyang Ma
- Proc. Amer. Math. Soc. 149 (2021), 1875-1887
- DOI: https://doi.org/10.1090/proc/15403
- Published electronically: February 23, 2021
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Abstract:
In this paper, we follow an idea of Lusztig to define the Fourier transform on the Ringel–Hall algebra of a valued quiver (given by a quiver with automorphism). As an application, this provides a direct proof of the fact that the Ringel–Hall algebra of a valued quiver is independent of its orientation. Furthermore, by combining the BGP-reflection operators defined on double Ringel–Hall algebras of valued quivers with Fourier transforms, we obtain an alternative construction of Lusztig’s symmetries of the associated quantum enveloping algebras. This generalizes a result of Sevenhant and Van den Bergh in the quiver case.References
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Bibliographic Information
- Chenyang Ma
- Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
- ORCID: 0000-0002-3443-6721
- Email: mcy16@mails.tsinghua.edu.cn
- Received by editor(s): December 2, 2019
- Received by editor(s) in revised form: December 3, 2019, and June 29, 2020
- Published electronically: February 23, 2021
- Additional Notes: This work was supported by the Natural Science Foundation of China (Grant No. 11971255).
- Communicated by: Jerzy Weyman
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1875-1887
- MSC (2020): Primary 16G20, 17B37
- DOI: https://doi.org/10.1090/proc/15403
- MathSciNet review: 4232183