In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over an arbitrary commutative ring.
Révisé le :
Accepté le :
Publié le :
Keywords: Quiver representations, Rigid representations, Lattices over orders
Crawley-Boevey, William  1
CC-BY 4.0
@article{ART_2024__1_3_375_0,
author = {Crawley-Boevey, William},
title = {Rigid integral representations of quivers over arbitrary commutative rings},
journal = {Annals of Representation Theory},
pages = {375--384},
year = {2024},
publisher = {The Publishers of ART},
volume = {1},
number = {3},
doi = {10.5802/art.15},
language = {en},
url = {https://www.numdam.org/articles/10.5802/art.15/}
}
TY - JOUR AU - Crawley-Boevey, William TI - Rigid integral representations of quivers over arbitrary commutative rings JO - Annals of Representation Theory PY - 2024 SP - 375 EP - 384 VL - 1 IS - 3 PB - The Publishers of ART UR - https://www.numdam.org/articles/10.5802/art.15/ DO - 10.5802/art.15 LA - en ID - ART_2024__1_3_375_0 ER -
%0 Journal Article %A Crawley-Boevey, William %T Rigid integral representations of quivers over arbitrary commutative rings %J Annals of Representation Theory %D 2024 %P 375-384 %V 1 %N 3 %I The Publishers of ART %U https://www.numdam.org/articles/10.5802/art.15/ %R 10.5802/art.15 %G en %F ART_2024__1_3_375_0
Crawley-Boevey, William. Rigid integral representations of quivers over arbitrary commutative rings. Annals of Representation Theory, Tome 1 (2024) no. 3, pp. 375-384. doi: 10.5802/art.15
[1] From triangulated categories to cluster algebras. II, Ann. Sci. Éc. Norm. Supér., Volume 39 (2006) no. 6, pp. 983-1009 | DOI | MR | Zbl | Numdam
[2] Exceptional sequences of representations of quivers, Representations of algebras (Ottawa, ON, 1992) (CMS Conference Proceedings), Volume 14, American Mathematical Society, 1993, pp. 117-124 | MR | Zbl
[3] Rigid integral representations of quivers, Representation theory of algebras (Cocoyoc, 1994) (CMS Conference Proceedings), Volume 18, American Mathematical Society, 1996, pp. 155-163 | MR | Zbl
[4] Subrepresentations of general representations of quivers, Bull. Lond. Math. Soc., Volume 28 (1996) no. 4, pp. 363-366 | DOI | MR | Zbl
[5] Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Paris; North-Holland, 1970 (avec un appendice Corps de classes local par Michiel Hazewinkel) | MR | Zbl
[6] Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150, Springer, 1995 | DOI | MR | Zbl
[7] Rigid modules and Schur roots, Math. Z., Volume 295 (2020) no. 3-4, pp. 1245-1277 | DOI | MR | Zbl
[8] Exceptional bundles on surfaces with a moving anticanonical class, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 52 (1988) no. 4, p. 740-757, 895 | DOI | MR | Zbl
[9] Tilted algebras, Trans. Am. Math. Soc., Volume 274 (1982) no. 2, pp. 399-443 | DOI | MR | Zbl
[10] A categorification of non-crossing partitions, J. Eur. Math. Soc., Volume 18 (2016) no. 10, pp. 2273-2313 | DOI | MR | Zbl
[11] Serre’s problem on projective modules, Springer Monographs in Mathematics, Springer, 2006 | DOI | MR
[12] Exceptional collections, mutations and helices, Helices and vector bundles (London Mathematical Society Lecture Note Series), Volume 148, Cambridge University Press, 1990, pp. 1-6 | DOI | MR | Zbl
[13] General representations of quivers, Proc. Lond. Math. Soc., Volume 65 (1992) no. 1, pp. 46-64 | DOI | MR | Zbl
Cité par Sources :





