Reduction techniques for the finitistic dimension
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- by Edward L. Green, Chrysostomos Psaroudakis and Øyvind Solberg PDF
- Trans. Amer. Math. Soc. 374 (2021), 6839-6879 Request permission
Abstract:
In this paper we develop new reduction techniques for testing the finiteness of the finitistic dimension of a finite dimensional algebra over a field. Viewing the latter algebra as a quotient of a path algebra, we propose two operations on the quiver of the algebra, namely arrow removal and vertex removal. The former gives rise to cleft extensions and the latter to recollements. These two operations provide us new practical methods to detect algebras of finite finitistic dimension. We illustrate our methods with many examples.References
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Additional Information
- Edward L. Green
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
- MR Author ID: 76495
- ORCID: 0000-0003-0281-3489
- Email: green@math.vt.edu
- Chrysostomos Psaroudakis
- Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
- MR Author ID: 1041820
- Email: chpsaroud@math.auth.gr
- Øyvind Solberg
- Affiliation: Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway
- Email: oyvind.solberg@math.ntnu.no
- Received by editor(s): January 2, 2019
- Received by editor(s) in revised form: August 17, 2020
- Published electronically: July 15, 2021
- Additional Notes: The second author was supported by Deutsche Forschungsgemeinschaft (DFG, grant KO $1281/14-1$). The third author was partially supported by FRINAT grant number 23130 from the Norwegian Research Council
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 6839-6879
- MSC (2020): Primary 16E10, 16E30, 16G20, 18E10, 18G20
- DOI: https://doi.org/10.1090/tran/8409
- MathSciNet review: 4315591