Title:
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Recollement of colimit categories and its applications (English) |
Author:
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Huang, Ju |
Author:
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Chen, QingHua |
Author:
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Lai, Chunhuan |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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70 |
Issue:
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4 |
Year:
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2020 |
Pages:
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1147-1160 |
Summary lang:
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English |
. |
Category:
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math |
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Summary:
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We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and $K$-groups. (English) |
Keyword:
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colimit category |
Keyword:
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recollement |
Keyword:
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Leavitt path algebra |
Keyword:
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$K_i$ group |
MSC:
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18A30 |
MSC:
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19D50 |
idZBL:
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07285986 |
idMR:
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MR4181803 |
DOI:
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10.21136/CMJ.2020.0240-19 |
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Date available:
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2020-11-18T09:49:27Z |
Last updated:
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2023-01-02 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/148418 |
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Reference:
|
[1] Abrams, G., Pino, G. Aranda: The Leavitt path algebra of a graph.J. Algebra 293 (2005), 319-334. Zbl 1119.16011, MR 2172342, 10.1016/j.jalgebra.2005.07.028 |
Reference:
|
[2] Hügel, L. Angeleri, Koenig, S., Liu, Q.: Recollements and tilting objects.J. Pure Appl. Algebra 215 (2011), 420-438. Zbl 1223.18008, MR 2738361, 10.1016/j.jpaa.2010.04.027 |
Reference:
|
[3] Ara, P., Moreno, M. A., Pardo, E.: Nonstable $K$-theory for graph algebras.Algebr. Represent. Theory 10 (2007), 157-178. Zbl 1123.16006, MR 2310414, 10.1007/s10468-006-9044-z |
Reference:
|
[4] Asadollahi, J., Hafezi, R., Vahed, R.: On the recollements of functor categories.Appl. Categ. Struct. 24 (2016), 331-371. Zbl 1360.18020, MR 3516076, 10.1007/s10485-015-9399-6 |
Reference:
|
[5] Barot, M., Lenzing, H.: One-point extensions and derived equivalence.J. Algebra 264 (2003), 1-5. Zbl 1060.16011, MR 1980681, 10.1016/S0021-8693(03)00124-8 |
Reference:
|
[6] Beilinson, A. A., Bernstein, J., Deligne, P.: Faisceaux pervers.Analysis and Topology on Singular Spaces I Astérisque 100. Société Mathématique de France, Paris (1982), 5-171 French. Zbl 1390.14055, MR 0751966 |
Reference:
|
[7] Bergman, G. M.: Direct limits and fixed point sets.J. Algebra 292 (2005), 592-614. Zbl 1088.18001, MR 2172170, 10.1016/j.jalgebra.2005.08.002 |
Reference:
|
[8] Chen, Q., Lin, Y.: Recollements of extension algebras.Sci. China, Ser. A 46 (2003), 530-537. Zbl 1215.18014, MR 2014485, 10.1007/BF02884025 |
Reference:
|
[9] Cline, E., Parshall, B., Scott, L.: Algebraic stratification in representation categories.J. Algebra 117 (1988), 504-521. Zbl 0659.18011, MR 0957457, 10.1016/0021-8693(88)90123-8 |
Reference:
|
[10] Franjou, V., Pirashvili, T.: Comparison of abelian categories recollements.Doc. Math. 9 (2004), 41-56. Zbl 1060.18008, MR 2054979 |
Reference:
|
[11] Fuchs, L., Göbel, R., Salce, L.: On inverse-direct systems of modules.J. Pura Appl. Algebra 214 (2010), 322-331. Zbl 1181.13009, MR 2558741, 10.1016/j.jpaa.2009.05.003 |
Reference:
|
[12] Grothendieck, A.: Groupes de classes des categories abeliennes et triangulees. Complexes parfaits.Séminaire de Géométrie Algébrique du Bois-Marie 1965-66 SGA 5 Lecture Notes in Mathematics 589. Springer, Berlin (1977), 351-371 French. Zbl 0345.00011, MR 0491704, 10.1007/BFb0096809 |
Reference:
|
[13] Guo, X. J., Li, L. B.: $K_1$ group of finite dimensional path algebra.Acta Math. Sin., Engl. Ser. 17 (2001), 273-276. Zbl 0986.19002, MR 1830928, 10.1007/s101149900010 |
Reference:
|
[14] Happel, D.: Reduction techniques for homological conjectures.Tsukuba J. Math. 17 (1993), 115-130. Zbl 0809.16021, MR 1233117, 10.21099/tkbjm/1496162134 |
Reference:
|
[15] Li, L. P.: Derived equivalences between triangular matrix algebras.Commun. Algebra 46 (2018), 615-628. Zbl 06875436, MR 3764883, 10.1080/00927872.2017.1327051 |
Reference:
|
[16] Mahmood, S. J.: Limimts and colimits in categories of d. g. near-rings.Proc. Edinb. Math. Soc., II. Ser. 23 (1980), 1-7. Zbl 0414.16023, MR 0582016, 10.1017/S0013091500003539 |
Reference:
|
[17] Miyachi, J.: Localization of triangulated categories and derived categories.J. Algebras 141 (1991), 463-483. Zbl 0739.18006, MR 1125707, 10.1016/0021-8693(91)90243-2 |
Reference:
|
[18] Parshall, B. J., Scott, L. L.: Derived categories, quasi-hereditary algebras, and algebraic groups.Proceedings of the Ottawa-Moosonee Workshop in Algebra Mathematical Lecture Note Series. Carlton University, Ottawa (1988), 1-104. Zbl 0711.18002 |
Reference:
|
[19] Quillen, D.: Higher algebraic $K$-theory. I.Higher $K$-Theories Lecture Notes in Mathematics 341. Springer, Berlin (1973). Zbl 0292.18004, MR 0338129, 10.1007/BFb0067053 |
Reference:
|
[20] Xue, R., Yan, Y., Chen, Q.: On colimit-categories.J. Math., Wuhan Univ. 32 (2012), 439-446. Zbl 1265.18002, MR 2963903 |
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