Stratifications of Finite Directed Categories and Generalized APR Tilting Modules

REFERENCES

• Assem , I. , Simson , D. , Skowronski , A. ( 2006 ). Elements of Representation Theory: Volume 1, Techniques of Representation Theory. Lond. Math. Soc. Student Texts, Vol. 65. Cambridge Univ. Press .
   Google Scholar
• Auslander , M. , Reiten , I. , Smalø , S. ( 1997 ). Representation Theory of Artin Algebras. Cambridge Studies in Adv. Math., Vol. 36. Cambridge Univ. Press .
   Google Scholar
• Auslander , M. , Platzeck , M. , Reiten , I. ( 1979 ). Coxeter functors without diagrams . Tran. Amer. Math. Soc. 250 : 1 – 46 .
   Web of Science ®Google Scholar
• Bautista , R. , Gabriel , P. , Roiter , A. V. , Salmerón , L. ( 1985 ). Representation-finite algebras and multiplicative bases . Invent. Math. 81 : 217 – 285 .
   Web of Science ®Google Scholar
• Burgess , W. , Fuller , K. , Tonolo , A. ( 2001 ). A note on block triangular presentations of rings and finitistic dimension . Rend. Sem. Mat. Univ. Padova 105 : 207 – 214 .
   Google Scholar
• Cline , E. , Parshall , B. , Scott , L. ( 1996 ). Stratifying Endomorphism algebras . Mem. Amer. Math. Soc. 124 ( 591 ).
   Web of Science ®Google Scholar
• tom Dieck , T. ( 1987 ). Transformation groups. de Gruyter Studies in Math., Vol. 8. Walter de Gruyter .
   Google Scholar
• Dietrich , K. ( 2010 ). Representation theory of EI categories. Ph.D. Thesis, Univ. of Paderborn .
   Google Scholar
• Dlab , V. , Ringel , C. ( 1992 ). The module theoretical approach to Quasi-hereditary Algebras. Representations of Algebras and Related Topics (Kyoto, 1990). Lond. Math. Soc. Lecture Note Ser., Vol. 168. Cambridge Univ. Press, pp. 200–224 .
   Google Scholar
• Erdmann , K. , Sáenz , C. (2003). On standardly stratified algebras. Comm. Algebras 31:3429–3446.
   Web of Science ®Google Scholar
• Happel , D. ( 1987 ). Triangulated Categories in Representation Theory of Finite-Dimensional Algebras. Lond. Math. Soc. Lecture Note Ser., Vol. 119. Cambridge Univ. Press .
   Google Scholar
• Happel , D. , Reiten , I. , Smalø , S. ( 1996 ). Piecesise hereditary algebras . Arch. Math. 66 : 182 – 186 .
   Web of Science ®Google Scholar
• Li , L. ( 2011 ). A characterization of finite EI categories with hereditary category algebras . J. Algebra 345 : 213 – 241 .
   Web of Science ®Google Scholar
• Li , L. ( 2014 ). On the representation types of finite EI categories . J. Algebra 402 : 178 – 218 .
   Web of Science ®Google Scholar
• Li , L. ( 2014 ). A generalized Koszul theory and its application . Trans. Amer. Math. Soc. 366 : 931 – 977 .
   Web of Science ®Google Scholar
• Li , L. ( 2013 ). Extension algebras of standard modules . Comm. Algebra 41 : 3445 – 3464 .
   Web of Science ®Google Scholar
• Li , L. ( 2013 ). Algebras stratified for all linear orders . Alg. Rep. Theory 16 : 1085 – 1108 .
   Web of Science ®Google Scholar
• Linckelmann , M. ( 2004 ). Fusion category algebras . J. Algebra 277 : 222 – 235 .
   Web of Science ®Google Scholar
• Lück , W. ( 1989 ). Transformation Groups and Algebraic K-Theory. Lecture Notes in Math., Vol. 1408. Springer-Verlag .
   Google Scholar
• Platzeck , M. , Reiten , I. ( 2001 ). Modules of finite projective dimension for standardly stratified algebras . Comm. Algebra 29 : 973 – 986 .
   Web of Science ®Google Scholar
• Ringel , C. ( 1991 ). The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences . Math. Z. 208 : 209 – 223 .
   Web of Science ®Google Scholar
• Webb , P. ( 2007 ). An introduction to the representations and cohomology of categories . In: M. , Testerman , D. , Thvenaz , J. (eds)., Group Representation Theory . Geck , EPFL Press (Lausanne) , pp. 149 – 173 .
   Google Scholar
• Webb , P. ( 2008 ). Standard stratifications of EI categories and Alperin's weight conjecture . J. Algebra 320 : 4073 – 4091 .
   Web of Science ®Google Scholar
• Xi , C. ( 2002 ). Standardly stratified algebras and cellular algebras . Math. Proc. Camb. Phil. Soc. 133 : 37 – 53 .
   Web of Science ®Google Scholar
• Xu , F. ( 2007 ). Representations of categories and their applications . J. Algebra 317 : 153 – 183 .
   Web of Science ®Google Scholar
• Xu , F. ( 2014 ). Support varieties for transporter category algebras . J. Pure Algebra 218 ( 4 ): 583 – 601 .
   Web of Science ®Google Scholar
• Communicated by D. Zacharia.
   Google Scholar