[AA18] Takahide Adachi and Toshitaka Aoki. The number of two-term tilting complexes over symmetric algebras with radical cube zero. arXiv preprint arXiv:1805.08392, 2018.
[AAC18] Takahide Adachi, Takuma Aihara, and Aaron Chan. Classification of two-term tilting complexes over Brauer graph algebras. Math.Z., 290(1-2):1–36, 2018.
[AAG08] Diana Avella-Alaminos and Christof Geiss. Combinatorial derived invariants for gentle algebras. J. Pure Appl. Algebra, 212(1):228– 243, 2008.
[Ada16a] Takahide Adachi. Characterizing τ -tilting finite algebras with radical square zero. Proc. Amer. Math. Soc., 144(11):4673–4685, 2016.
[Ada16b] Takahide Adachi. The classification of τ -tilting modules over Nakayama algebras. J. Algebra, 452:227–262, 2016.
[ADI] Sota Asai, Laurent Demonet, and Osamu Iyama. On algebras with dense g-vector cones. in preparation.
[AH81] Ibrahim Assem and Dieter Happel. Generalized tilted algebras of type An. Comm. Algebra, 9(20):2101–2125, 1981.
[AI12] Takuma Aihara and Osamu Iyama. Silting mutation in triangulated categories. J. Lond. Math. Soc. (2), 85(3):633–668, 2012.
[Aih13] Takuma Aihara. Tilting-connected symmetric algebras. Algebr. Represent. Theory, 16(3):873–894, 2013.
[Aih14] Takuma Aihara. Mutating Brauer trees. Math. J. Okayama Univ., 56:1–16, 2014.
[Aih15] Takuma Aihara. Derived equivalences between symmetric special biserial algebras. J. Pure Appl. Algebra, 219(5):1800–1825, 2015.
[AIR14] Takahide Adachi, Osamu Iyama, and Idun Reiten. τ -tilting theory. Compos. Math., 150(3):415–452, 2014.
[ALP16] Kristin Krogh Arnesen, Rosanna Laking, and David Pauksztello. Morphisms between indecomposable complexes in the bounded derived category of a gentle algebra. J. Algebra, 467:1–46, 2016.
[AMN20] Hideto Asashiba, Yuya Mizuno, and Ken Nakashima. Simplicial complexes and tilting theory for Brauer tree algebras. J. Algebra, 551:119–153, 2020.
[Aok] Toshitaka Aoki. Brauer tree algebras have 2nntwo-term tilting complexes. in preparation.
[Aok18] Toshitaka Aoki. Classifying torsion classes for algebras with radical square zero via sign decomposition. arXiv preprint arXiv:1803.03795, 2018.
[APR79] Maurice Auslander, Mar´ıa In´es Platzeck, and Idun Reiten. Coxeter functors without diagrams. Trans. Amer. Math. Soc., 250:1–46, 1979.
[APS19] Claire Amiot, Pierre-Guy Plamondon, and Sibylle Schroll. A complete derived invariant for gentle algebras via winding numbers and Arf invariants. arXiv preprint arXiv:1904.02555, 2019.
[ARS95] Maurice Auslander, Idun Reiten, and Sverre O. Smalø. Representation theory of Artin algebras, volume 36 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1995.
[AS87] Ibrahim Assem and Andrzej Skowro´nski. Iterated tilted algebras of type A˜ n. Math. Z., 195(2):269–290, 1987.
[Asa19] Sota Asai. The wall-chamber structures of the real Grothendieck groups. arXiv preprint arXiv:1905.02180, 2019.
[ASS06] Ibrahim Assem, Daniel Simson, and Andrzej Skowro´nski. Elements of the representation theory of associative algebras. Vol. 1, volume 65 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2006. Techniques of representation theory.
[AY] Toshitaka Aoki and Toshiya Yurikusa. Complete special biserial algebras are g-tame. arXiv preprint arXiv:2003.09797v2.
[BB80] Sheila 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), volume 832 of Lecture Notes in Math., pages 103–169. Springer, Berlin-New York, 1980.
[BBD82] A. A. Be˘ılinson, J. Bernstein, and P. Deligne. Faisceaux pervers. In Analysis and topology on singular spaces, I (Luminy, 1981), volume 100 of Ast´erisque, pages 5–171. Soc. Math. France, Paris, 1982.9
[Ben08] David J. Benson. Resolutions over symmetric algebras with radical cube zero. J. Algebra, 320(1):48–56, 2008.
[BGP73] I. N. Bernsteın, I. M. Gelfand, and V. A. Ponomarev. Coxeter functors, and Gabriel’s theorem. Uspehi Mat. Nauk, 28(2(170)):19–33,1973.
[BGS04] Grzegorz Bobi´nski, Christof Geiß, and Andrzej Skowro´nski. Classification of discrete derived categories. Cent. Eur. J. Math., 2(1):19– 49, 2004.
[BM03] Viktor Bekkert and H´ector A. Merklen. Indecomposables in derived categories of gentle algebras. Algebr. Represent. Theory, 6(3):285– 302, 2003.
[BMR+06] Aslak Bakke Buan, Robert Marsh, Markus Reineke, Idun Reiten, and Gordana Todorov. Tilting theory and cluster combinatorics. Adv. Math., 204(2):572–618, 2006.
[Bon81] Klaus Bongartz. Tilted algebras. In Representations of algebras (Puebla, 1980), volume 903 of Lecture Notes in Math., pages 26–38. Springer, Berlin-New York, 1981.
[BPP16] Nathan Broomhead, David Pauksztello, and David Ploog. Discrete derived categories II: the silting pairs CW complex and the stability manifold. J. Lond. Math. Soc. (2), 93(2):273–300, 2016.
[BR87] M. C. R. Butler and Claus Michael Ringel. Auslander-Reiten sequences with few middle terms and applications to string algebras. Comm. Algebra, 15(1-2):145–179, 1987.
[BR18] Emily Barnard and Nathan Reading. Coxeter-biCatalan combinatorics. J. Algebraic Combin., 47(2):241–300, 2018.
[Bri07] Tom Bridgeland. Stability conditions on triangulated categories. Ann. of Math. (2), 166(2):317–345, 2007.
[Bri17] Tom Bridgeland. Scattering diagrams, Hall algebras and stability conditions. Algebr. Geom., 4(5):523–561, 2017.
[BS15] Tom Bridgeland and Ivan Smith. Quadratic differentials as stability conditions. Publ. Math. Inst. Hautes Etudes Sci. ´ , 121:155–278, 2015.
[BST19] Thomas Br¨ustle, David Smith, and Hipolito Treffinger. Wall and chamber structure for finite-dimensional algebras. Adv. Math., 354:106746, 31, 2019.
[BY13] Thomas Br¨ustle and Dong Yang. Ordered exchange graphs. In Advances in representation theory of algebras, EMS Ser. Congr. Rep., pages 135–193. Eur. Math. Soc., Z¨urich, 2013.
[CB89] W. W. Crawley-Boevey. Maps between representations of zerorelation algebras. J. Algebra, 126(2):259–263, 1989.
[CD20] Aaron Chan and Laurent Demonet. Classifying torsion classes of gentle algebras. arXiv preprint arXiv:2009.10266v1, 2020.
[CL12] Sabin Cautis and Anthony Licata. Heisenberg categorification and Hilbert schemes. Duke Math. J., 161(13):2469–2547, 2012.
[CR62] Charles W. Curtis and Irving Reiner. Representation theory of finite groups and associative algebras. Pure and Applied Mathematics, Vol. XI. Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962.
[DF15] Harm Derksen and Jiarui Fei. General presentations of algebras. Adv. Math., 278:210–237, 2015.
[DIJ19] Laurent Demonet, Osamu Iyama, and Gustavo Jasso. τ -tilting finite algebras, bricks, and g-vectors. Int. Math. Res. Not. IMRN, 2019(3):852–892, 2019.
[DIR+18] Laurent Demonet, Osamu Iyama, Nathan Reading, Idun Reiten, and Hugh Thomas. Lattice theory of torsion classes. arXiv preprint arXiv:1711.01785v2, 2018.
[DR74] Vlastimil Dlab and Claus Michael Ringel. Representations of graphs and algebras. Department of Mathematics, Carleton University, Ottawa, Ont., 1974. Carleton Mathematical Lecture Notes, No. 8.
[EJR18] Florian Eisele, Geoffrey Janssens, and Theo Raedschelders. A reduction theorem for τ -rigid modules. Math.Z., 290(3-4):1377–1413, 2018.
[ES11] Karin Erdmann and Øyvind Solberg. Radical cube zero weakly symmetric algebras and support varieties. J. Pure Appl. Algebra, 215(2):185–200, 2011.
[FT18] Sergey Fomin and Dylan Thurston. Cluster algebras and triangulated surfaces Part II: Lambda lengths. Mem. Amer. Math. Soc., 255(1223):v+97, 2018.
[FZ07] Sergey Fomin and Andrei Zelevinsky. Cluster algebras. IV. Coefficients. Compos. Math., 143(1):112–164, 2007.
[Gab72] Peter Gabriel. Unzerlegbare Darstellungen. I. Manuscripta Math., 6:71–103; correction, ibid. 6 (1972), 309, 1972.
[GS16] Edward L. Green and Sibylle Schroll. Multiserial and special multiserial algebras and their representations. Adv. Math., 302:1111–1136, 2016.
[GS17] Edward L. Green and Sibylle Schroll. Brauer configuration algebras: a generalization of Brauer graph algebras. Bull. Sci. Math., 141(6):539–572, 2017.
[Hap88] Dieter Happel. Triangulated categories in the representation theory of finite-dimensional algebras, volume 119 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1988.
[Hil06] L. Hille. On the volume of a tilting module. Abh. Math. Sem. Univ. Hamburg, 76:261–277, 2006.
[HK01] Ruth Stella Huerfano and Mikhail Khovanov. A category for the adjoint representation. J. Algebra, 246(2):514–542, 2001.
[HKK17] F. Haiden, L. Katzarkov, and M. Kontsevich. Flat surfaces and stability structures. Publ. Math. Inst. Hautes Etudes Sci. ´ , 126:247– 318, 2017.
[HKM02] Mitsuo Hoshino, Yoshiaki Kato, and Jun-Ichi Miyachi. On tstructures and torsion theories induced by compact objects. J. Pure Appl. Algebra, 167(1):15–35, 2002.
[HRS96] Dieter Happel, Idun Reiten, and Sverre O. Smalø. Tilting in abelian categories and quasitilted algebras. Mem. Amer. Math. Soc., 120(575):viii+ 88, 1996.
[HU05] Dieter Happel and Luise Unger. On a partial order of tilting modules. Algebr. Represent. Theory, 8(2):147–156, 2005.
[IJY14] Osamu Iyama, Peter Jørgensen, and Dong Yang. Intermediate co-tstructures, two-term silting objects, τ -tilting modules, and torsion classes. Algebra Number Theory, 8(10):2413–2431, 2014.
[Kau98] Michael Kauer. Derived equivalence of graph algebras. In Trends in the representation theory of finite-dimensional algebras (Seattle, WA, 1997), volume 229 of Contemp. Math., pages 201–213. Amer. Math. Soc., Providence, RI, 1998.
[Kim20] Yuta Kimura. Tilting theory of noetherian algebras. arXiv preprint arXiv:2006.01677, 2020.
[KM19] Yuta Kimura and Yuya Mizuno. Two-term tilting complexes for preprojective algebras of non-dynkin type. arXiv preprint arXiv:1908.02424, 2019.
[KS02] Mikhail Khovanov and Paul Seidel. Quivers, Floer cohomology, and braid group actions. J. Amer. Math. Soc., 15(1):203–271, 2002.
[KY14] Steffen Koenig and Dong Yang. Silting objects, simple-minded collections, t-structures and co-t-structures for finite-dimensional algebras. Doc. Math., 19:403–438, 2014.
[Lab13] Fran¸cois Labourie. Lectures on representations of surface groups. Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Z¨urich, 2013.
[LP20] Yankı Lekili and Alexander Polishchuk. Derived equivalences of gentle algebras via Fukaya categories. Math. Ann., 376(1-2):187– 225, 2020.
[Nak18] Hiroyuki Nakaoka. Finite gentle repetitions of gentle algebras and their Avella-Alaminos–Geiss invariants. arXiv preprint arXiv:1811.00775v1, 2018.
[Oku86] Tetsuro Okuyama. On blocks of finite groups with radical cube zero. Osaka J. Math., 23(2):461–465, 1986.
[ONFR15] Mustafa A. A. Obaid, S. Khalid Nauman, Wafaa M. Fakieh, and Claus Michael Ringel. The number of support-tilting modules for a Dynkin algebra. J. Integer Seq., 18(10):Article 15.10.6, 24, 2015.
[Opp19] Sebastian Opper. On auto-equivalences and complete derived invariants of gentle algebras. arXiv preprint arXiv:1904.04859v1, 2019.
[OPS18] Sebastian Opper, Pierre-Guy Plamondon, and Sibylle Schroll. A geometric model for the derived category of gentle algebras. arXiv preprint arXiv:1801.09659v5, 2018.
[PPP19] Yann Palu, Vincent Pilaud, and Pierre-Guy Plamondon. Nonkissing and non-crossing complexes for locally gentle algebras. J. Comb. Algebra, 3(4):401–438, 2019.
[Qiu16] Yu Qiu. Decorated marked surfaces: spherical twists versus braid twists. Math. Ann., 365(1-2):595–633, 2016.
[Ric89] Jeremy Rickard. Morita theory for derived categories. J. London Math. Soc. (2), 39(3):436–456, 1989.
[Sch18] Sibylle Schroll. Brauer graph algebras: a survey on Brauer graph algebras, associated gentle algebras and their connections to cluster theory. In Homological methods, representation theory, and cluster algebras, CRM Short Courses, pages 177–223. Springer, Cham, 2018.
[Sei08] Paul Seidel. Fukaya categories and Picard-Lefschetz theory. Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Z¨urich, 2008.
[ST01] Paul Seidel and Richard Thomas. Braid group actions on derived categories of coherent sheaves. Duke Math. J., 108(1):37–108, 2001.
[Voß01] Dieter Voßieck. The algebras with discrete derived category. J. Algebra, 243(1):168–176, 2001.
[WW85] Burkhard Wald and Josef Waschb¨usch. Tame biserial algebras. J. Algebra, 95(2):480–500, 1985.
[Yur18] Toshiya Yurikusa. Wide subcategories are semistable. Doc. Math., 23:35–47, 2018.
[Yur20] Toshiya Yurikusa. Density of g-vector cones from triangulated surfaces. Int. Math. Res. Not. IMRN, rnaa008, 2020.
[Zha13] Xiaojin Zhang. τ -rigid modules for algebras with radical square zero. arXiv preprint arXiv:1211.5622, 2013.