| Title:
|
Piecewise hereditary algebras under field extensions (English) |
| Author:
|
Li, Jie |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1025-1034 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $A$ be a finite-dimensional $k$-algebra and $K/k$ be a finite separable field extension. We prove that $A$ is derived equivalent to a hereditary algebra if and only if so is $A\otimes _kK$. (English) |
| Keyword:
|
piecewise hereditary algebra |
| Keyword:
|
Galois extension |
| Keyword:
|
directing object |
| MSC:
|
16E35 |
| MSC:
|
16G10 |
| idZBL:
|
Zbl 07442471 |
| idMR:
|
MR4339108 |
| DOI:
|
10.21136/CMJ.2021.0183-20 |
| . |
| Date available:
|
2021-11-08T15:59:32Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149235 |
| . |
| Reference:
|
[1] Assem, I., Simson, D., Skowrońsky, A.: Elements of the Representation Theory of Associative Algebras. Vol. 1. Techniques of Representation Theory.London Mathematical Society Student Texts 65. Cambridge University Press, Cambridge (2006). Zbl 1092.16001, MR 2197389, 10.1017/CBO9780511614309 |
| Reference:
|
[2] Chen, X.-W., Ringel, C. M.: Hereditary triangulated categories.J. Noncommut. Geom. 12 (2018), 1425-1444. Zbl 1430.18010, MR 3896230, 10.4171/JNCG/311 |
| Reference:
|
[3] Dionne, J., Lanzilotta, M., Smith, D.: Skew group algebras of piecewise hereditary algebras are piecewise hereditary.J. Pure Appl. Algebra 213 (2009), 241-249. Zbl 1166.16005, MR 2467401, 10.1016/j.jpaa.2008.06.010 |
| Reference:
|
[4] Happel, D., Reiten, I.: Hereditary abelian categories with tilting object over arbitrary base fields.J. Algebra 256 (2002), 414-432. Zbl 1015.18007, MR 1939113, 10.1016/S0021-8693(02)00088-1 |
| Reference:
|
[5] Happel, D., Zacharia, D.: A homological characterization of piecewise hereditary algebras.Math. Z. 260 (2008), 177-185. Zbl 1193.16005, MR 2413349, 10.1007/s00209-007-0268-3 |
| Reference:
|
[6] Kasjan, S.: Auslander-Reiten sequences under base field extension.Proc. Am. Math. Soc. 128 (2000), 2885-2896. Zbl 0974.16012, MR 1670379, 10.1090/S0002-9939-00-05382-X |
| Reference:
|
[7] Li, J.: Algebra extensions and derived-discrete algebras.Available at https://arxiv.org/abs/1904.07168 (2019), 8 pages. |
| Reference:
|
[8] Li, L.: Finitistic dimensions and piecewise hereditary property of skew group algebras.Glasg. Math. J. 57 (2015), 509-517. Zbl 1336.16022, MR 3395330, 10.1017/S0017089514000445 |
| Reference:
|
[9] Lin, Y., Zhou, Z.: Tilted algebras and crossed products.Glasg. Math. J. 58 (2016), 559-571. Zbl 1372.16009, MR 3530486, 10.1017/S0017089515000336 |
| Reference:
|
[10] Năstăsescu, C., Bergh, M. Van den, Oystaeyen, F. Van: Separable functors applied to graded rings.J. Algebra 123 (1989), 397-413. Zbl 0673.16026, MR 1000494, 10.1016/0021-8693(89)90053-7 |
| Reference:
|
[11] Rafael, M. D.: Separable functors revisited.Commun. Algebra 18 (1990), 1445-1459. Zbl 0713.18002, MR 1059740, 10.1080/00927879008823975 |
| Reference:
|
[12] Rickard, J.: Morita theory for derived categories.J. Lond. Math. Soc., II. Ser. 39 (1989), 436-456. Zbl 0642.16034, MR 1002456, 10.1112/jlms/s2-39.3.436 |
| Reference:
|
[13] Zimmermann, A.: A Noether-Deuring theorem for derived categories.Glasg. Math. J. 54 (2012), 647-654. Zbl 1258.16014, MR 2965408, 10.1017/S0017089512000237 |
| . |
