NTNU

Summer School 2001:
Homological conjectures for finite dimensional algebras

References for the lectures in the first part (preliminary version)

[AEJO] S. T. Aldrich, E. E. Enochs, O. M. G. Jenda, L. Oyonarte, Envelopes and covers by modules of finite injective and projective dimension, preprint
[AG] D. J. Anick, E. L. Green, On the homology of quotients of path algebras, Comm. in Alg., 15 (1987) 309-341.
[A] I. Assem, Tilting theory - an introduction, Topics in algebra, Banach Center Publications, vol. 26, part 1 (1990) 127-180.
[Au] M. Auslander, Representation dimension of artin algebras, Queen Mary College, Mathematics Notes, University of London (1971). Also in Selected works of Maurice Auslander, part 1, Amer. Math. Soc.
[AR1] M. Auslander, I. Reiten, Application of contravariantly finite subcategories, Adv. Math., vol. 86, no. 1 (1991) 111-152
[AR2] M. Auslander, I. Reiten, Homological finite subcategories, Representations of algebras and related topics (Tsukuba, 1990), 1--42, London Math. Soc. Lecture Note Ser., 168, Cambridge Univ. Press, Cambridge, 1992.
[AS] M. Auslander, S. O. Smalø, Preprojective modules over Artin algebras, J. Algebra 66 (1980), no. 1, 61-122.
[B] H. Bass, Injective dimension in Noetherian rings, Trans. AMS 102 (1962) 18-29.
[BH] W. Bruns, J. Herzog, Cohen-Macaulay rings, Cambridge studies in advanced mathematics 39, Cambridge University Press.
[BK] M. C. R. Butler, A. King, Minimal resolutions of algebras, J. Algebra, 212 (1999), no. 1, 323-362.
[E] D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995. xvi+785 pp. ISBN: 0-387-94268-8; 0-387-94269-6
[G] P. Gabriel, Finite representation type is open, Proceedings of the International Conference on Representations of Algebras (Carleton Univ., Ottawa, Ont., 1874) Paper no. 10, 23pp., Carleton Math. Lecture Notes, No. 9, Carleton Univ., 1974.
[G1] E. L. Green, Multiplicative bases, Gröbner bases, and right Gröbner bases, Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998). J. Symbolic Comput. 29 (2000), no. 4-5, 601-623.
[G2] E. L. Green, Noncommutative Gröbner bases and projective resolutions Computational methods for representations of groups and algebras (Essen, 1997), 29-60, Progr. Math., 173, Birkhäuser, Basel, 1999.
[GKK] E. L. Green, E. Kirkman, J. Kuzmanovich, Finitistic dimensions of finite dimensional monomial algebras, J. Algebra 136 (1991), no. 1, 37-50.
[GR] L. Gruson, L. Raynaud, Critères de platitude et de projectivité. Techniques de "platification" d'un module, Invent. Math. 13 (1971) 1-89.
[GSZ] E. L. Green, Ø. Solberg, D. Zacharia, Minimal projective resolutions, Trans. Amer. Math., to appear.
[H1] D. Happel, Homological conjectures in representation theory of finite-dimensional algebras, (DVI-file, PS-file) Sherbrooke lecture notes series
[H2] D. Happel, Reduction techiques for homological conjectures, Tsukuba J., 17 (1993) 115-130
[H3] D. Happel, Triangulated categories in the representation theory of finite dimensional algebras, London Math. Soc., Lecture Note Series 119, Cambridge University Press.
[HZ] B. Huisgen-Zimmermann, Homological domino effects and the first finitistic dimension conjecture, Invent. Math. 108 (1992) 369-383
[HZ2] B. Zimmermann Huisgen, The finitistic dimension conjectures - A tale of 3.5 decades, Abelian groups and modules (Padova, 1994), 501--517, Math. Appl., 343, Kluwer Acad. Publ., Dordrecht, 1995
[HZS] B. Zimmermann Huisgen, S. O. Smalø, A homological bridge between finite- and infinite-dimensional representations of algebras, Algebr. Represent. Theory 1 (1998), no. 2, 169-188.
[IST] K. Igusa, S. O. Smalø, G. Todorov, Finite projectivity and contravariant finiteness, Proc. Amer. Math. Soc. 109 (1990), no. 4, 937-941.
[K1] B. Keller, Derivation and tilting, Algebra VIII
[K2] B. Keller, On the construction of triangle equivlances, in Derived equivalences for group rings, Springer Lecture Notes 1685
[K3] B. Keller, Introduction to abelian and derived categories, Preprint
[Kr] H. Krause, Finistic dimension and Ziegler spectrum, Proc. Amer. Math. Soc. 126 (1998), no. 4, 983-987.
[KS] H. Krause, Ø. Solberg, Filtering modules of finite projective dimension, preprint.
[MHS] F. H. Membrillo-Hernandez, L. Salmeron, A geometric approach to the finististic dimension conjecture, Arch. Math. vol. 67 (1996) 448-456
[S] S. O. Smalø, The supremum of the difference between the big and little finitistic dimensions is infinite, Proc. Amer. Math. Soc. 126 (1998), no. 9, 2619-2622
[W] Y. Wang, A note on the finitistic dimension conjecture, Comm. Alg., 22 (1994) no. 7, 2525-2528
[X1] C. Xi, On the representation dimension of finite dimensional algebras, J. Algebra 226 (2000) 332-346
[X2] C. Xi, Representation dimension and quasi-hereditary algebras,

Further references, incomplete at this point

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