Minimal bipartite algebras of infinite prinjective type with prin-preprojective component

• Autorzy: Stanisław Kasjan
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 76
• Numer: 2
• Strony: 295-317

Daty

wydano

1998

otrzymano

1997-06-02

poprawiono

1997-10-29

Twórcy

autor

Stanisław Kasjan

• Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] M. Auslander, I. Reiten and S. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995.
• [2] K. Bongartz, Algebras and quadratic forms, J. London Math. Soc. 28 (1983), 461-469.
• [3] K. Bongartz, Critical simply connected algebras, Manuscripta Math. 46 (1984), 177-136.
• [4] D Yu. A. Drozd, Matrix problems and the category of matrices, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 28 (1978), 144-153 (in Russian).
• [5] D. Happel and D. Vossieck, Minimal algebras of infinite representation type with preprojective component, Manuscripta Math. 42 (1983), 221-243.
• [6] H.-J. von Höhne, On weakly non-negative unit forms and tame algebras, Proc. London Math. Soc. 73 (1996), 47-67.
• [7] H.-J. von Höhne and D. Simson, Bipartite posets of finite prinjective type, J. Algebra (1998), in press.
• [8] S. Kasjan, On prinjective modules, tameness and Tits form, Bull. Polish Acad. Sci. Math. 41 (1993), 327-341.
• [9] S. Kasjan and D. Simson, Fully wild prinjective type of posets and their quadratic forms, J. Algebra 172 (1995), 506-529.
• [10] O S. A. Ovsienko, Integral weakly positive unit forms, in: Schur Matrix Problems and Quadratic Forms, Kiev, 1978, 3-17 (in Russian).
• [11] J. A. de la Pe na, Quadratic forms and the representation type of an algebra, SFB 343, Diskrete Strukturen in der Mathematik, preprint 90-003, Bielefeld, 1990.
• [12] J. A. de la Pe na, Coxeter transformations and the representation theory of algebras, in: Finite-Dimensional Algebras and Related Topics, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424, 1994, 223-253.
• [13] J. A. de la Pena and D. Simson, Prinjective modules, reflection functors, quadratic forms, and Auslander-Reiten sequences, Trans. Amer. Math. Soc. 329 (1992), 733-753.
• [14] C. M. Ringel, Representations of K-species and bimodules, J. Algebra 41 (1976), 269-302.
• [15] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
• [16] C. M. Ringel, The spectral radius of the Coxeter transformations for a generalized Cartan matrix, Math. Ann. 300 (1994), 331-339.
• [17] D. Simson, Moduled categories and adjusted modules over traced rings, Dissertationes Math. 269 (1990).
• [18] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, 1992.
• [19] D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra 90 (1993), 77-103.
• [20] D. Simson, Representation embedding problems, categories of extensions and prinjective modules, in: Proc. Seventh Internat. Conf. on Representations of Algebras, Canad. Math. Soc. Conf. Proc. 18, 1996, 601-639.
• [21] D. Simson, Prinjective modules, propartite modules, representations of bocses and lattices over orders, J. Math. Soc. Japan 49 (1997), 31-68.
• [22] D. Simson, Three-partite subamalgams of tiled orders of finite lattice type, J. Pure Appl. Algebra (1998), in press.
• [23] A. Skowroński, Generalized standard Auslander-Reiten components, J. Math. Soc. Japan 46 (1994), 518-543.
• [24] D. Vossieck, Représentations de bifoncteurs et interprétations en termes de modules, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), 713-716.
• [25] T. Weichert, Darstellungstheorie von Algebren mit projektivem Sockel, Doctoral thesis, Universität Stuttgart, 1989.