Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
approximation; derived equivalence; subring; endomorphism algebra; Auslander-Yoneda algebra
approximation; derived equivalence; subring; endomorphism algebra; Auslander-Yoneda algebra
Summary:
We investigate derived equivalences between subalgebras of some $\Phi $-Auslander-Yoneda algebras from a class of $n$-angles in weakly $n$-angulated categories. The derived equivalences are obtained by transferring subalgebras induced by $n$-angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to $n$-angle cases. Finally, we give an explicit example to illustrate our result.
References:
[1] Aihara, T., Iyama, O.: Silting mutation in triangulated categories. J. Lond. Math. Soc., II. Ser. 85 (2012), 633-668. DOI 10.1112/jlms/jdr055 | MR 2927802 | Zbl 1271.18011
[2] Brüstle, T., Pan, S.: Transfer of derived equivalences from subalgebras to endomorphism algebras. J. Algebra Appl. 15 (2016), Article ID 1650100, 10 pages. DOI 10.1142/S0219498816501000 | MR 3479804 | Zbl 1345.18010
[3] Buan, A. B., Marsh, R. B., Reineke, M., Reiten, I., Todorov, G.: Tilting theory and cluster combinatorics. Adv. Math. 204 (2006), 572-618. DOI 10.1016/j.aim.2005.06.003 | MR 2249625 | Zbl 1127.16011
[4] Chen, Y.: Derived equivalences in $n$-angulated categories. Algebr. Represent. Theory 16 (2013), 1661-1684. DOI 10.1007/s10468-012-9377-8 | MR 3127353 | Zbl 1291.18016
[5] Chen, Y.: Derived equivalences between subrings. Commun. Algebra 42 (2014), 4055-4065. DOI 10.1080/00927872.2013.804925 | MR 3200079 | Zbl 1312.16004
[6] Chen, Y., Hu, W.: Approximations, ghosts and derived equivalences. Proc. R. Soc. Edinb., Sect. A, Math. 150 (2020), 813-840. DOI 10.1017/prm.2018.120 | MR 4080461 | Zbl 1442.18033
[7] Fedele, F.: Auslander-Reiten $(d+2)$-angles in subcategories and a $(d+2)$-angulated generalisation of a theorem by Brüning. J. Pure App. Algebra 223 (2019), 3354-3580. DOI 10.1016/j.jpaa.2018.11.017 | MR 3926227 | Zbl 1411.16017
[8] Geiss, C., Keller, B., Oppermann, S.: $n$-angulated categories. J. Reine Angew. Math. 675 (2013), 101-120. DOI 10.1515/CRELLE.2011.177 | MR 3021448 | Zbl 1271.18013
[9] Happel, D., Unger, L.: Complements and the generalized Nakayama conjecture. Algebras and Modules. II CMS Conference Proceedings 24. AMS, Providence (1998), 293-310. MR 1648633 | Zbl 0944.16010
[10] Hoshino, M., Kato, Y.: An elementary construction of tilting complexes. J. Pure Appl. Algebra 177 (2003), 159-175. DOI 10.1016/S0022-4049(02)00176-7 | MR 1954331 | Zbl 1012.18006
[11] Hu, W., Koenig, S., Xi, C.: Derived equivalences from cohomological approximations and mutations of $\Phi$-Yoneda algebras. Proc. R. Soc. Edinb., Sect. A, Math. 143 (2013), 589-629. DOI 10.1017/S030821051100045X | MR 3063574 | Zbl 1336.16014
[12] Hu, W., Xi, C.: $D$-split sequences and derived equivalences. Adv. Math. 227 (2011), 292-318. DOI 10.1016/j.aim.2011.01.023 | MR 2782196 | Zbl 1260.16017
[13] Hu, W., Xi, C.: Derived equivalences for $\Phi$-Auslander-Yoneda algebras. Trans. Am. Math. Soc. 365 (2013), 5681-5711. DOI 10.1090/S0002-9947-2013-05688-7 | MR 3091261 | Zbl 1279.18008
[14] Iyama, O., Oppermann, S.: $n$-representation-finite algebras and $n$-APR tilting. Trans. Am. Math. Soc. 363 (2011), 6575-6614. DOI 10.1090/S0002-9947-2011-05312-2 | MR 2833569 | Zbl 1264.16015
[15] Iyama, O., Yoshino, Y.: Mutation in triangulated categories and rigid Cohen-Macaulay modules. Invent. Math. 172 (2008), 117-168. DOI 10.1007/s00222-007-0096-4 | MR 2385669 | Zbl 1140.18007
[16] Karoubi, M.: Algèbres de Clifford et K-théorie. Ann. Sci. Éc. Norm. Supér. (4) 1 (1968), 161-270 French. DOI 10.24033/asens.1163 | MR 0238927 | Zbl 0194.24101
[17] Neeman, A.: Triangulated Categories. Annals of Mathematics Studies 148. Princeton University Press, Princeton (2001). DOI 10.1515/9781400837212 | MR 1812507 | Zbl 0974.18008
[18] Pan, S.: Symmetric approximation sequences, Beilinson-Green algebras and derived equivalences. Math. Scand. 128 (2022), 451-506. DOI 10.7146/math.scand.a-133541 | MR 4529806 | Zbl 1531.16009
[19] Rickard, J.: Derived categories and stable equivalence. J. Pure Appl. Algebra 61 (1989), 303-317. DOI 10.1016/0022-4049(89)90081-9 | MR 1027750 | Zbl 0685.16016
[20] Rickard, J.: Derived equivalences as derived functors. J. Lond. Math. Soc., II. Ser. 43 (1991), 37-48. DOI 10.1112/jlms/s2-43.1.37 | MR 1099084 | Zbl 0683.16030
[21] Rudakov, A. N.: Exceptional collections, mutations and helices. Helices and Vector Bundles London Mathematical Society Lecture Note Series 148. Cambridge Univerity Press, Cambridge (1990), 1-6. DOI 10.1017/CBO9780511721526.001 | MR 1074777 | Zbl 0721.14011
[22] Xi, C.: On the finitistic dimension conjecture. I: Related to representation-finite algebras. J. Pure Appl. Algebra 193 (2004), 287-305. DOI 10.1016/j.jpaa.2004.03.009 | MR 2076389 | Zbl 1067.16016
Search
Partner of
