Deformations of bimodule problems
Geiß, Christof
Fundamenta Mathematicae, Tome 149 (1996), p. 255-264 / Harvested from The Polish Digital Mathematics Library

We prove that deformations of tame Krull-Schmidt bimodule problems with trivial differential are again tame. Here we understand deformations via the structure constants of the projective realizations which may be considered as elements of a suitable variety. We also present some applications to the representation theory of vector space categories which are a special case of the above bimodule problems.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:212176
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     author = {Christof Gei\ss },
     title = {Deformations of bimodule problems},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {255-264},
     zbl = {0859.16010},
     language = {en},
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Geiß, Christof. Deformations of bimodule problems. Fundamenta Mathematicae, Tome 149 (1996) pp. 255-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i3p255bwm/

[00000] [1] K. Bongartz, On degenerations and extensions of finite-dimensional modules, Adv. in Math., to appear. | Zbl 0862.16007

[00001] [2] W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. 56 (1988), 451-483. | Zbl 0661.16026

[00002] [3] W. W. Crawley-Boevey, Functorial filtrations II: clans and the Gelfand problem, J. London Math. Soc. 40 (1989), 9-30. | Zbl 0725.16012

[00003] [4] W. W. Crawley-Boevey, Matrix problems and Drozd's theorem, in: Topics in Algebra, Part 1: Rings and Representations of Algebras, Banach Center Publ. 26, PWN, Warszawa, 1990, 199-222.

[00004] [5] Yu. A. Drozd, Tame and wild matrix problems, in: Representation Theory II, Lecture Notes in Math. 832, Springer, 1980, 242-258.

[00005] [6] Yu. A. Drozd and G. M. Greuel, Tame-wild dichotomy for Cohen-Macaulay modules, Math. Ann. 294 (1992), 387-394. | Zbl 0760.16005

[00006] [7] P. Gabriel, Finite representation type is open, in: Representations of Algebras, Lecture Notes in Math. 488, Springer, 1975, 132-155.

[00007] [8] P. Gabriel, L. A. Nazarova, A. V. Roiter, V. V. 1Sergejchuk and D. Vossieck, Tame and wild subspace problems, Ukrain. Math. J. 45 (1993), 313-352.

[00008] [9] P. Gabriel and A. V. Roiter, Representations of Finite-Dimensional Algebras, Encyclopedia of Math. Sci. 73, Algebra VIII, Springer, 1992.

[00009] [10] C. Geiß, Tame distributive algebras and related topics, Dissertation, Universität Bayreuth, 1993.

[00010] [11] C. Geiß, On degenerations of tame and wild algebras, Arch. Math. (Basel) 64 (1995), 11-16. | Zbl 0828.16013

[00011] [12] R. Hartshorne, Algebraic Geometry, Springer, 1977.

[00012] [13] H. Kraft and C. Riedtmann, Geometry of representations of quivers, in: Representations of Algebras, London Math. Soc. Lecture Note Ser. 116, Cambridge Univ. Press, 1985, 109-145. | Zbl 0632.16019

[00013] [14] J. A. de la Pe na, On the dimension of module varieties of tame and wild algebras, Comm. Algebra 19 (1991), 1795-1805. | Zbl 0818.16013

[00014] [15] J. A. de la Pe na, Functors preserving tameness, Fund. Math. 137 (1991), 77-185. | Zbl 0790.16014

[00015] [16] J. A. de la Pe na and D. Simson, Preinjective modules, reflection functors, quadratic forms, and Auslander-Reiten sequences, Trans. Amer. Math. Soc. 329 (1992), 733-753. | Zbl 0789.16010

[00016] [17] C. M. Ringel, Tame algebras, in: Representation Theory I, Lecture Notes in Math. 831, Springer, 1980, 134-287.

[00017] [18] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.

[00018] [19] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, 1992. | Zbl 0818.16009