Quasi-hereditary algebras with all standard modules being isomorphic to submodules of projective modules

References

[1] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Grad. Texts in Math. 13, Springer, New York, 1992. 10.1007/978-1-4612-4418-9Search in Google Scholar

[2] M. Auslander and M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. 94, American Mathematical Society, Providence, 1969. 10.1090/memo/0094Search in Google Scholar

[3] M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge University, Cambridge, 1995. 10.1017/CBO9780511623608Search in Google Scholar

[4] C. Bowman and S. Martin, A reciprocity result for projective indecomposable modules of cellular algebras and BGG algebras, J. Lie Theory 22 (2012), no. 4, 1065–1073. Search in Google Scholar

[5] J. Chuang and K. M. Tan, Representations of wreath products of algebras, Math. Proc. Cambridge Philos. Soc. 135 (2003), no. 3, 395–411. 10.1017/S0305004103006984Search in Google Scholar

[6] E. Cline, B. Parshall and L. Scott, Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 85–99. 10.1515/crll.1988.391.85Search in Google Scholar

[7] B. M. Deng and C. C. Xi, Quasi-hereditary algebras which are dual extensions of algebras, Comm. Algebra 22 (1994), no. 12, 4717–4735. 10.1080/00927879408825097Search in Google Scholar

[8] B. M. Deng and C. C. Xi, Quasi-hereditary algebras which are twisted double incidence algebras of posets, Beitr. Algebra Geom. 36 (1995), no. 1, 37–71. Search in Google Scholar

[9] D. I. Deriziotis, The submodule structure of Weyl modules for groups of type A 1 , Comm. Algebra 9 (1981), no. 3, 247–265. 10.1080/00927878108822577Search in Google Scholar

[10] R. Dipper and G. James, q-tensor space and q-Weyl modules, Trans. Amer. Math. Soc. 327 (1991), no. 1, 251–282. 10.1090/S0002-9947-1991-1012527-1Search in Google Scholar

[11] V. Dlab and C. M. Ringel, Quasi-hereditary algebras, Illinois J. Math. 33 (1989), no. 2, 280–291. 10.1215/ijm/1255988725Search in Google Scholar

[12] V. Dlab and C. M. Ringel, The module theoretical approach to quasi-hereditary algebras, Representations of Algebras and Related Topics, London Math. Soc. Lecture Note Ser. 168, Cambridge University, Cambridge (1992), 200–224. 10.1017/CBO9780511661853.007Search in Google Scholar

[13] S. Donkin, On Schur algebras and related algebras. IV. The blocks of the Schur algebras, J. Algebra 168 (1994), no. 2, 400–429. 10.1006/jabr.1994.1236Search in Google Scholar

[14] S. Donkin, The q-Schur Algebra, London Math. Soc. Lecture Note Ser. 253, Cambridge University, Cambridge, 1998. 10.1017/CBO9780511600708Search in Google Scholar

[15] S. Donkin and I. Reiten, On Schur algebras and related algebras. V. Some quasi-hereditary algebras of finite type, J. Pure Appl. Algebra 97 (1994), no. 2, 117–134. 10.1016/0022-4049(94)90056-6Search in Google Scholar

[16] S. R. Doty, K. Erdmann, S. Martin and D. K. Nakano, Representation type of Schur algebras, Math. Z. 232 (1999), no. 1, 137–182. 10.1007/PL00004755Search in Google Scholar

[17] K. Erdmann, Schur algebras of finite type, Quart. J. Math. Oxford Ser. (2) 44 (1993), no. 173, 17–41. 10.1093/qmath/44.1.17Search in Google Scholar

[18] K. Erdmann and A. Henke, On Ringel duality for Schur algebras, Math. Proc. Cambridge Philos. Soc. 132 (2002), no. 1, 97–116. 10.1017/S0305004101005485Search in Google Scholar

[19] K. Erdmann and D. K. Nakano, Representation type of q-Schur algebras, Trans. Amer. Math. Soc. 353 (2001), no. 12, 4729–4756. 10.1090/S0002-9947-01-02849-5Search in Google Scholar

[20] M. Fang, Permanents, Doty coalgebras and dominant dimension of Schur algebras, Adv. Math. 264 (2014), 155–182. 10.1016/j.aim.2014.07.005Search in Google Scholar

[21] M. Fang and S. Koenig, Schur functors and dominant dimension, Trans. Amer. Math. Soc. 363 (2011), no. 3, 1555–1576. 10.1090/S0002-9947-2010-05177-3Search in Google Scholar

[22] M. Fang and H. Miyachi, Hochschild cohomology and dominant dimension, Trans. Amer. Math. Soc. 371 (2019), no. 8, 5267–5292. 10.1090/tran/7704Search in Google Scholar

[23] D. J. Hemmer and D. K. Nakano, Specht filtrations for Hecke algebras of type A, J. Lond. Math. Soc. (2) 69 (2004), no. 3, 623–638. 10.1112/S0024610704005186Search in Google Scholar

[24] J. E. Humphreys, Representations of Semisimple Lie Algebras in the BGG Category 𝒪 , Grad. Stud. Math. 94, American Mathematical Society, Providence, 2008. 10.1090/gsm/094Search in Google Scholar

[25] R. S. Irving, BGG algebras and the BGG reciprocity principle, J. Algebra 135 (1990), no. 2, 363–380. 10.1016/0021-8693(90)90294-XSearch in Google Scholar

[26] G. D. James, The decomposition of tensors over fields of prime characteristic, Math. Z. 172 (1980), no. 2, 161–178. 10.1007/BF01182401Search in Google Scholar

[27] S. Koenig, J. Külshammer and S. Ovsienko, Quasi-hereditary algebras, exact Borel subalgebras, A ∞ -categories and boxes, Adv. Math. 262 (2014), 546–592. 10.1016/j.aim.2014.05.016Search in Google Scholar

[28] S. König, Exact Borel subalgebras of quasi-hereditary algebras. I, Math. Z. 220 (1995), no. 3, 399–426. 10.1007/BF02572622Search in Google Scholar

[29] S. König, Exact Borel subalgebras of quasi-hereditary algebras. II, Comm. Algebra 23 (1995), no. 6, 2331–2344. 10.1080/00927879508825348Search in Google Scholar

[30] S. König, On the global dimension of quasi-hereditary algebras with triangular decomposition, Proc. Amer. Math. Soc. 124 (1996), no. 7, 1993–1999. 10.1090/S0002-9939-96-03549-6Search in Google Scholar

[31] R. Marczinzik, Simple reflexive modules over Artin algebras, J. Algebra Appl. 18 (2019), no. 10, Article ID 1950193. 10.1142/S0219498819501937Search in Google Scholar

[32] V. Mazorchuk and S. Ovsienko, Finitistic dimension of properly stratified algebras, Adv. Math. 186 (2004), no. 1, 251–265. 10.1016/j.aim.2003.08.001Search in Google Scholar

[33] C. M. Ringel, The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences, Math. Z. 208 (1991), no. 2, 209–223. 10.1007/BF02571521Search in Google Scholar

[34] C. M. Ringel, Simple reflexive modules over finite-dimensional algebras, J. Algebra Appl. 20 (2021), no. 9, Article ID 2150166. 10.1142/S0219498821501668Search in Google Scholar

[35] J. J. Rotman, An Introduction to Homological Algebra, 2nd ed., Universitext, Springer, New York, 2008. 10.1007/b98977Search in Google Scholar

[36] R. Rouquier, q-Schur algebras and complex reflection groups, Mosc. Math. J. 8 (2008), no. 1, 119–158, 184. 10.17323/1609-4514-2008-8-1-119-158Search in Google Scholar

[37] H. Tachikawa, Quasi-Frobenius Rings and Generalizations. QF - 3 and QF - 1 Rings, Lecture Notes in Math. 351, Springer, Berlin, 1973. 10.1007/BFb0059997Search in Google Scholar

[38] C. Wang and C. Xi, Finitistic dimension conjecture and radical-power extensions, J. Pure Appl. Algebra 221 (2017), no. 4, 832–846. 10.1016/j.jpaa.2016.08.006Search in Google Scholar

[39] Q. Wang, On τ-tilting finiteness of the Schur algebra, J. Pure Appl. Algebra 226 (2022), no. 1, Article ID 106818. 10.1016/j.jpaa.2021.106818Search in Google Scholar

[40] C. C. Xi, Quasi-hereditary algebras with a duality, J. Reine Angew. Math. 449 (1994), 201–215. 10.1515/crll.1994.449.201Search in Google Scholar