Homological invariants of the arrow removal operation
HTML articles powered by AMS MathViewer
- by Karin Erdmann, Chrysostomos Psaroudakis and Øyvind Solberg
- Represent. Theory 26 (2022), 370-387
- DOI: https://doi.org/10.1090/ert/606
- Published electronically: March 23, 2022
- PDF | Request permission
Abstract:
In this paper we show that Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology are invariants under the arrow removal operation for a finite dimensional algebra.References
- Maurice Auslander and Idun Reiten, Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), no. 1, 111–152. MR 1097029, DOI 10.1016/0001-8708(91)90037-8
- Apostolos Beligiannis, Cleft extensions of abelian categories and applications to ring theory, Comm. Algebra 28 (2000), no. 10, 4503–4546. MR 1780016, DOI 10.1080/00927870008827104
- R.-O. Buchweitz, Maximal Cohen-Macaulay modules and Tate-cohomology over Gorenstein rings, unpublished manuscript (1986), http://hdl.handle.net/1807/16682.
- Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos, and Andrea Solotar, Deleting or adding arrows of a bound quiver algebra and Hochschild (co)homology, Proc. Amer. Math. Soc. 148 (2020), no. 6, 2421–2432. MR 4080885, DOI 10.1090/proc/14936
- Karin Erdmann, Miles Holloway, Rachel Taillefer, Nicole Snashall, and Øyvind Solberg, Support varieties for selfinjective algebras, $K$-Theory 33 (2004), no. 1, 67–87. MR 2199789, DOI 10.1007/s10977-004-0838-7
- Karin Erdmann and Øyvind Solberg, Radical cube zero weakly symmetric algebras and support varieties, J. Pure Appl. Algebra 215 (2011), no. 2, 185–200. MR 2720683, DOI 10.1016/j.jpaa.2010.04.012
- Edward L. Green, Chrysostomos Psaroudakis, and Øyvind Solberg, Reduction techniques for the finitistic dimension, Trans. Amer. Math. Soc. 374 (2021), no. 10, 6839–6879. MR 4315591, DOI 10.1090/tran/8409
- Chrysostomos Psaroudakis, Øystein Skartsæterhagen, and Øyvind Solberg, Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements, Trans. Amer. Math. Soc. Ser. B 1 (2014), 45–95. MR 3274657, DOI 10.1090/S2330-0000-2014-00004-6
- The QPA-team, QPA2-Quivers, path algebras and representations, https://github.sunnyquiver/QPA2.
- Øyvind Solberg, Support varieties for modules and complexes, Trends in representation theory of algebras and related topics, Contemp. Math., vol. 406, Amer. Math. Soc., Providence, RI, 2006, pp. 239–270. MR 2258047, DOI 10.1090/conm/406/07659
- Fei Xu, Hochschild and ordinary cohomology rings of small categories, Adv. Math. 219 (2008), no. 6, 1872–1893. MR 2455628, DOI 10.1016/j.aim.2008.07.014
Bibliographic Information
- Karin Erdmann
- Affiliation: Karin Erdmann, Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB, England
- MR Author ID: 63835
- ORCID: 0000-0002-6288-0547
- Email: erdmann@maths.ox.ac.uk
- 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@ntnu.no
- Received by editor(s): September 20, 2021
- Received by editor(s) in revised form: December 23, 2021
- Published electronically: March 23, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Represent. Theory 26 (2022), 370-387
- MSC (2020): Primary 18Exx, 16E30, 16E65; Secondary 16E10, 16Gxx
- DOI: https://doi.org/10.1090/ert/606
- MathSciNet review: 4398475