ALMOST SPLIT SEQUENCES FOR COMPLEXES VIA RELATIVE HOMOLOGY

다국어 초록 (Multilingual Abstract)

We use methods of relative homological algebra on the category C(modΛ), of complexes of finitely generated modules over an artin algebra Λ, to give some characterizations of almost split sequences.

참고문헌 (Reference)

1 D. Happel, "Triangulated categories in the representation theory of finite dimensional al-gebras" Cambridge University Press 119 : 1988

2 H. Krause, "The Auslander-Reiten formula for complexes of modules" 207 (207): 133-148, 2006

3 P. Gabriel, "Representations of finite dimensional algebras, In Algebra VIII" Springer 73 : 1992

4 M. Auslander, "Representation theory of Artin algebras. III. Almost split sequences" 3 (3): 239-294, 1975

5 M. Auslander, "Representation Theory of Artin Algebras" Cambridge Univ. Press 1995

6 M. Auslander, "Relative homology and representation theory I. Relative homology and homologically finite subcategories" 21 (21): 2995-3031, 1993

7 D. Happel, "On the derived category of a finite dimensional algebras" 63 (63): 339-389, 1987

8 X. Zhang, "On F-almost split sequences" 26 (26): 1149-1164, 2010

9 P. Zhang, "Monomorphism categories, cotilting theory, and Gorenstein-projective mod-ules" 339 : 181-202, 2011

10 P. Ng, "Existence of Auslander-Reiten sequences in subcategories" 215 (215): 2378-2384, 2011

11 P. Dr¨axler, "Exact categories and vector space categories" 351 (351): 647-682, 1999

12 I. Assem, "Elements of the Representation Theory of Associative Algebras Vol. I" Cambridge University Press 65 : 2006

13 J.-L. Verdier, "Des cat´egories d´eriv´ees des cat´egories ab´eliennes" 239 : 253-, 1996

14 M. Auslander, "Comments on the functor Ext" 8 : 151-166, 1969

15 E. E. Enochs, "Cartan-Eilenberg complexes and resolutions" 342 : 16-39, 2011

16 P. Jorgensen, "Auslander-Reiten triangles in subcategories" 3 (3): 583-601, 2009

17 H. Lenzing, "Auslander-Reiten duality for abelian categories" 10 (10): 169-177, 2004

18 M. Kleiner, "Approximations and almost split sequences in homologically finite subcate-gories" 198 (198): 135-163, 1997

19 R. Bautista, "Almost split sequences of complexes of fixed size" 287 (287): 140-168, 2005

20 S. Salarian, "Almost split sequences in the category of complexes of modules" 14 (14): 15-, 2015

21 M. Auslander, "Almost split sequences in subcategories" 69 (69): 426-454, 1981

22 S. Liu, "Almost split sequences and approximations" 16 (16): 1809-1827, 2013