Catenarity in quantum nilpotent algebras
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- by K. R. Goodearl and S. Launois HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 7 (2020), 202-214
Abstract:
In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any two given prime ideals $P \subsetneq Q$ have the same length. This is achieved by proving that the prime spectra of these algebras have normal separation, and then establishing the mild homological conditions necessary to apply a result of Lenagan and the first author. The work also recovers the Tauvel height formula for quantum nilpotent algebras, a result that was first obtained by Lenagan and the authors through a different approach.References
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Additional Information
- K. R. Goodearl
- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 75245
- Email: goodearl@math.ucsb.edu
- S. Launois
- Affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, CT2 7FS, United Kingdom
- MR Author ID: 727444
- ORCID: 0000-0001-7252-8515
- Email: S.Launois@kent.ac.uk
- Received by editor(s): August 1, 2020
- Received by editor(s) in revised form: October 16, 2020
- Published electronically: December 16, 2020
- Additional Notes: The research of the first-named author was supported by U.S. National Science Foundation grant DMS-1601184. That of the second-named author was supported by EPSRC grant EP/N034449/1.
- Communicated by: Sarah Witherspoon
- © Copyright 2020 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 7 (2020), 202-214
- MSC (2020): Primary 16T20; Secondary 16D25, 16P40, 16S36, 20G42
- DOI: https://doi.org/10.1090/bproc/65
- MathSciNet review: 4188200