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Book Information

Author(s): Dieter Happel
Title: Triangulated categories in the representation theory of finite dimensional algebras
Additional book information: Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, 1988. (London Mathematical Society Lecture Notes Series, vol. 119), ix + 208 pp., $24.95. ISBN 0-521-33922-7

1.: I. Assem and D. Happel, Generalized tilted algebras of type A, Comm. Algebra 9 (1981), 2101-2125. MR 640613
2.: I. Assem, D. Happel and O. Roldán, Representation-finite trivial extension algebras, J. Pure. Appl. Algebra 33 (1984), 235-242. MR 761629
3.: I. Assem and A. Skowroński, Algebras with cycle-finite derived categories, Math. Ann. 280 (1988), 441-463. MR 936322
4.: M. Auslander and I. Reiten, Representation theory of artin algebras. III and IV, Comm. Algebra 3 (1975), 239-294 and 5 (1977), 443-518. MR 439881
5.: A. A. Beilinson, Coherent sheaves on P and problems of linear algebra, Functional Anal. Appl. 12 (1978), 214-216. MR 509388
6.: A. A. Beilinson, J. Bernstein and P. Deligne, Faisceaux pervers, Astérisque 100 (1982). MR 751966
7.: I. N. Bernstein, I. M. Gelfand and S. I. Gelfand, Algebraic bundles over P and problems of linear algebra, Functional Anal. Appl. 12 (1978), 212-214.
8.: I. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, Coxeter functors and Gabriel's theorem, Russian Math. Surveys 28 (1973), 17-32. MR 393065
9.: S. Brenner and M. C. R. Butler, Generalization of the Bernstein-Gelfand-Ponomarev reflection functors, Proc. ICRA II (Ottawa, 1979) Lecture Notes in Math., vol. 832, Springer-Verlag, Berlin and New York, 1980, pp. 103-169. MR 607151
10.: E. Cline, B. Parshall and L. Scott, Derived categories and Morita theory, J. Algebra 104 (1986), 397-409. MR 866784
11.: P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergeb. Math. Grenzgeb. Band 35, Springer-Verlag, Berlin and New York, 1967. MR 210125
12.: W. Geigle and H. Lenzing, A class of weighted projective curves arising in the representation theory of finite dimensional algebras, Proc. Lambrecht 1985, Lecture Notes in Math., vol. 1273, Springer-Verlag, Berlin and New York, 1987, pp. 265-297. MR 915180
13.: D. Happel, On the derived category of a finite dimensional algebra, Comment. Math. Helv. 62 (1987), 339-389. MR 910167
14.: D. Happel, Hochschild cohomology of finite dimensional algebras, preprint, University of Bielefeld, 1988. MR 1035222
15.: D. Happel, J. Rickard and A. Schofield, Piecewise hereditary algebras, Bull. London Math. Soc. 20 (1988), 23-28. MR 916069
16.: D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399-443. MR 675063
17.: D. Happel and C. M. Ringel, The derived category of a tubular algebra, Proc. ICRA IV (Ottawa 1984) Lecture Notes in Math., vol. 1177, Springer-Verlag, Berlin and New York, 1986, pp. 156-180. MR 842465
18.: R. Hartshorne, Residues and duality, Lecture Notes in Math., vol. 20, Springer-Verlag, Berlin and New York, 1966. MR 222093
19.: D. Hugues and J. Washbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. 46 (1983), 347-364. MR 693045
20.: B. Iversen, Cohomology of sheaves, Springer-Verlag, 1986. MR 842190
21.: M. M. Kapranov, Derived category of coherent sheaves on Grassman manifolds, Functional Anal. Appl. 17 (1983), 145-146. MR 705052
22.: Y. Miyashita, Tilting modules of finite projective dimension, Math. Z. 193 (1986), 113-146. MR 852914
23.: J. Rickard, A Morita theory for derived categories, preprint, University College London, 1987. MR 1002456
24.: J. Rickard, Derived categories and stable equivalence, preprint, University College London, 1987. MR 1027750
25.: C. M. Ringel, Tame algebras and integral quadratic forms, Lecture Notes in Math., vol. 1099, Springer-Verlag, Berlin and New York, 1984. MR 774589
26.: J.-L. Verdier, Catégories dérivées, état 0, Lecture Notes in Math., vol. 569, Springer-Verlag, Berlin and New York, 1977, pp. 262-311.
27.: T. Wakamatsu, Stable equivalence for self-injective algebras and a generalization of tilting modules, preprint, Jōbu University, 1988. MR 1074331

Review Information:
Journal: Bull. Amer. Math. Soc. 22 (1990), 153-158.
DOI: 10.1090/S0273-0979-1990-15869-0
PII: S 0273-0979(1990)15869-0

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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