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ON THE MODULE CATEGORIES OF GENERALIZED PREPROJECTIVE ALGEBRAS OF DYNKIN TYPE

Murakami, Kota 大阪大学 DOI:10.18910/87484

2022.04

概要

For a symmetrizable GCM C and its symmetrizer D, Geiss-Leclerc-Schr¨oer [Invent. Math. 209 (2017)] has introduced a generalized preprojective algebra Π associated to C and D, that contains a class of modules, called locally free modules. We show that any basic support τ- tilting Π-module is locally free and gives a classification theorem of torsion-free classes in repΠ as the generalization of the work of Mizuno [Math. Z. 277 (2014)].

参考文献

[1] T. Adachi, O. Iyama and I. Reiten: τ-tilting theory, Compos. Math. 150 (2014), 415–452.

[2] S. Asai: Bricks over preprojective algebras and join-irreducible elements in coxeter groups, 2017, arXiv:1712.08311.

[3] I. Assem, D. Simson and A. Skowronski: Elements of the representation theory of associative algebras. ´ Vol. 1, London Mathematical Society Student Texts 65, Cambridge University Press, Cambridge, 2006.

[4] P. Baumann, J. Kamnitzer and P. Tingley: Affine Mirkovi´c-Vilonen polytopes, Publ. Math. Inst. Hautes Etudes Sci. ´ 120 (2014), 113–205.

[5] A. Bjorner and F. Brenti: Combinatorics of Coxeter groups, Graduate Texts in Mathematics ¨ 231, Springer, New York, 2005.

[6] S. Brenner and M.C.R. Butler: Generalizations of the Bernstein-Gel’fand-Ponomarev reflection functors; in Representation theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math. 832, Springer, Berlin-New York, 1980, 103–169.

[7] A.B. Buan, O. Iyama, I. Reiten and J. Scott: Cluster structures for 2-Calabi-Yau categories and unipotent groups, Compos. Math. 145 (2009), 1035–1079.

[8] R.W. Carter: Lie algebras of finite and affine type, Cambridge Studies in Advanced Mathematics 96, Cambridge University Press, Cambridge, 2005.

[9] L. Demonet, O. Iyama and G. Jasso: τ-Tilting Finite Algebras, Bricks, and g-Vectors, Int. Math. Res. Not. IMRN 2019 (2019), 852–892.

[10] C. Fu and S. Geng: Tilting modules and support τ-tilting modules over preprojective algebras associated with symmetrizable Cartan matrices, Algebr. Represent. Theory 22 (2019), 1239–1260.

[11] P. Gabriel: Unzerlegbare Darstellungen. I, Manuscripta Math. 6 (1972), 71–103; correction, ibid. 6 (1972), 309.

[12] C. Geiß, B. Leclerc and J. Schroer: ¨ Kac-Moody groups and cluster algebras, Adv. Math. 228 (2011), 329–433.

[13] C. Geiss, B. Leclerc and J. Schroer: ¨ Quivers with relations for symmetrizable Cartan matrices I: Foundations, Invent. Math. 209 (2017), 61–158.

[14] I.M. Gelfand and V.A. Ponomarev: Model algebras and representations of graphs, Funktsional. Anal. I Prilozhen. 13 (1979), 1–12.

[15] D. Happel: Triangulated categories in the representation theory of finite-dimensional algebras, London Mathematical Society Lecture Note Series, 119, Cambridge University Press, Cambridge, 1988.

[16] O. Iyama, N. Reading, I. Reiten and H. Thomas: Lattice structure of Weyl groups via representation theory of preprojective algebras, Compos. Math. 154 (2018), 1269–1305.

[17] V.G. Kac: Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57–92.

[18] V.G. Kac: Infinite root systems, representations of graphs and invariant theory. II, J. Algebra 78 (1982), 141–162.

[19] Y. Kimura: Tilting theory of preprojective algebras and c-sortable elements, J. Algebra 503 (2018), 186– 221.

[20] Y. Miyashita: Tilting modules of finite projective dimension, Math. Z. 193 (1986), 113–146.

[21] Y. Mizuno: Classifying τ-tilting modules over preprojective algebras of Dynkin type, Math. Z. 277 (2014), 665–690.

[22] S. Oppermann, I. Reiten and H. Thomas: Quotient closed subcategories of quiver representations, Compos. Math. 151 (2015), 568–602.

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