The cohomology ring of a monomial algebra

manuscripta mathematica - Tập 85 - Trang 11-23 - 1994
E. L. Green1, D. Zacharia2
1Department of Mathematics Virginia Polytechnic Institute and State University, Blacksburg
2Department of Mathematics, Syracuse University, Syracuse

Tóm tắt

In this paper we study the algebra structure of the cohomology ring of a monomial algebra.

Tài liệu tham khảo

Anick, D.,Noncommutative graded algebras and their Hilbert series, Journal of Algebra78 (1982), pp. 120–140. Anick, D.,On monomial algebras of finite global dimension, Transactions AMS291 (1985), pp. 291–310 Anick, D. and Green, E.L.,On the homology of quotients of path algebras, Communications in Algebra, Vol. 15, Numbers 1 & 2, (1987), pp. 309–342. Avramov, L.,Obstructions to the existence of multiplicative structures on minimal free resolutions, American Journal of Mathematics103 (1981), pp. 1–31. Benson, D.J.,Representations and Cohomology, Cambridge Studies in Adv. Math.,31 (1991), Cambridge University Press. Carlson, J.,Varieties and the cohomology ring of a module, Journal of Algebra85 (1983), pp. 104–143 Cartan, H. and Eilenberg, S.,Homological Algebra, Princeton University Press, 1956. Cline, E., Parshall, B. and Scott, L.,The homological dual of a highest weight category. Preprint Erdmann, K.,Blocks of tame representation type and related algebras, Lecture Notes in Mathematics, Vol. 1428 (1990), Springer-Verlag Green, E.L.,Graphs with relations, coverings and group-graded algebras, Transactions AMS,279 (1983), pp. 297–310 Gabriel, P.,Auslander-Reiten sequences and representation finite algebras, Lecture Notes in Mathematics, Vol. 831 (1980), Springer-Verlag Green, E.L., Happel, D. and Zacharia, D.,Projective resolutions over artin algebras with zero relations, Illinois Journal of Mathematics,29, Number 1, (1983), pp. 80–190 Green, E.L., Kirkman, E. and Kuzmanovich, J.,Finitistic dimension of finite dimensional monomial algebras, Journal of Algebra136, (1991), pp. 37–50. Green, E.L. and Membrillo-Hernandez, F.H.,A finite dimensional algebra with cohomology ring not finitely generated, rch Math (to appear) Igusa, K. and Zacharia, D.,Syzygy pairs in a monomial algebra, Proceedings AMS,108 Number 3 (1990), pp. 601–604 Lescot, J.,Asymptotic properties of Betti numbers of modules over certain rings, Journal Pure and Applied Algebra,38 (1985), pp. 287–298 Löfall, C.,On the subalgebra generated by the one-dimensional elements in the Yoneda Ext-algebra, Lecture Notes in Mathematics, Vol. 1352 (1988), pp. 291–338 Manin, Yu. I.,Quantum Groups and Noncommutative Geometry, Centre de Recherche Math., Montreal, 1988 MacLane, S.,Homology, Springer-Verlag, 1963 Roos, J.E.,Relations between the Poincaré-Betti series of loop spaces and of local rings, lecture Notes in Mathematics, Vol. 740 (1979), Springer-Verlag, pp. 285–322