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Keywords:
colimit category; recollement; Leavitt path algebra; $K_i$ group
Summary:
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.
References:
[1] Abrams, G., Pino, G. Aranda: The Leavitt path algebra of a graph. J. Algebra 293 (2005), 319-334. DOI 10.1016/j.jalgebra.2005.07.028 | MR 2172342 | Zbl 1119.16011
[2] Hügel, L. Angeleri, Koenig, S., Liu, Q.: Recollements and tilting objects. J. Pure Appl. Algebra 215 (2011), 420-438. DOI 10.1016/j.jpaa.2010.04.027 | MR 2738361 | Zbl 1223.18008
[3] Ara, P., Moreno, M. A., Pardo, E.: Nonstable $K$-theory for graph algebras. Algebr. Represent. Theory 10 (2007), 157-178. DOI 10.1007/s10468-006-9044-z | MR 2310414 | Zbl 1123.16006
[4] Asadollahi, J., Hafezi, R., Vahed, R.: On the recollements of functor categories. Appl. Categ. Struct. 24 (2016), 331-371. DOI 10.1007/s10485-015-9399-6 | MR 3516076 | Zbl 1360.18020
[5] Barot, M., Lenzing, H.: One-point extensions and derived equivalence. J. Algebra 264 (2003), 1-5. DOI 10.1016/S0021-8693(03)00124-8 | MR 1980681 | Zbl 1060.16011
[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. MR 0751966 | Zbl 1390.14055
[7] Bergman, G. M.: Direct limits and fixed point sets. J. Algebra 292 (2005), 592-614. DOI 10.1016/j.jalgebra.2005.08.002 | MR 2172170 | Zbl 1088.18001
[8] Chen, Q., Lin, Y.: Recollements of extension algebras. Sci. China, Ser. A 46 (2003), 530-537. DOI 10.1007/BF02884025 | MR 2014485 | Zbl 1215.18014
[9] Cline, E., Parshall, B., Scott, L.: Algebraic stratification in representation categories. J. Algebra 117 (1988), 504-521. DOI 10.1016/0021-8693(88)90123-8 | MR 0957457 | Zbl 0659.18011
[10] Franjou, V., Pirashvili, T.: Comparison of abelian categories recollements. Doc. Math. 9 (2004), 41-56. MR 2054979 | Zbl 1060.18008
[11] Fuchs, L., Göbel, R., Salce, L.: On inverse-direct systems of modules. J. Pura Appl. Algebra 214 (2010), 322-331. DOI 10.1016/j.jpaa.2009.05.003 | MR 2558741 | Zbl 1181.13009
[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. DOI 10.1007/BFb0096809 | MR 0491704 | Zbl 0345.00011
[13] Guo, X. J., Li, L. B.: $K_1$ group of finite dimensional path algebra. Acta Math. Sin., Engl. Ser. 17 (2001), 273-276. DOI 10.1007/s101149900010 | MR 1830928 | Zbl 0986.19002
[14] Happel, D.: Reduction techniques for homological conjectures. Tsukuba J. Math. 17 (1993), 115-130. DOI 10.21099/tkbjm/1496162134 | MR 1233117 | Zbl 0809.16021
[15] Li, L. P.: Derived equivalences between triangular matrix algebras. Commun. Algebra 46 (2018), 615-628. DOI 10.1080/00927872.2017.1327051 | MR 3764883 | Zbl 06875436
[16] Mahmood, S. J.: Limimts and colimits in categories of d. g. near-rings. Proc. Edinb. Math. Soc., II. Ser. 23 (1980), 1-7. DOI 10.1017/S0013091500003539 | MR 0582016 | Zbl 0414.16023
[17] Miyachi, J.: Localization of triangulated categories and derived categories. J. Algebras 141 (1991), 463-483. DOI 10.1016/0021-8693(91)90243-2 | MR 1125707 | Zbl 0739.18006
[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
[19] Quillen, D.: Higher algebraic $K$-theory. I. Higher $K$-Theories Lecture Notes in Mathematics 341. Springer, Berlin (1973). DOI 10.1007/BFb0067053 | MR 0338129 | Zbl 0292.18004
[20] Xue, R., Yan, Y., Chen, Q.: On colimit-categories. J. Math., Wuhan Univ. 32 (2012), 439-446. MR 2963903 | Zbl 1265.18002
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