References
A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T U, V, W, X, Y, Z,
[Al79] | J. L. Alperin, Projective modules for [math]SL(2,2^n)[/math], J. Pure and Applied Algebra 15 (1979), 219-234. |
[Al80] | J. L. Alperin, Local representation theory, The Santa Cruz Conference on Finite Groups., Proc. Sympos. Pure Math. 37 (1980), 369-375. |
[AE81] | J. L. Alperin and L. Evens, Representations, resoluutions and Quillen's dimension theorem, J. Pure Appl. Algebra 22 (1981), 1-9. |
[AE04] | Jianbei An and C. W. Eaton, Blocks with trivial intersection defect groups, Math. Z. 247 (2004), 461-486. |
[Ar19] | C. G. Ardito, Morita equivalence classes of blocks with elementary abelian defect groups of order 32, arXiv:1908.02652 |
[ArMcK20] | C. G. Ardito and E. McKernon, 2-blocks with an abelian defect group and a freely acting cyclic inertial quotient, arxiv.org/abs/2010.08329 |
[AS20] | C. G. Ardito and B. Sambale, Broué's Conjecture for 2-blocks with elementary abelian defect groups of order 32, Preprint. |
[AKO11] | M. Aschbacher, R. Kessar and B. Oliver, Fusion systems in algebra and topology, London Mathematical Society Lecture Notes 391, Cambridge University Press (2011). |
[BK07] | D. Benson and R. Kessar, Blocks inequivalent to their Frobenius twists, J. Algebra 315 (2007), 588-599. |
[BKL18] | R. Boltje, R. Kessar, and M. Linckelmann, On Picard groups of blocks of finite groups, J. Algebra |
[Bra41] | R. Brauer, Investigations on group characters, Ann. Math. 42 (1941), 936-958. |
[BP80] | M. Broué and L. Puig, A Frobenius theorem for blocks, Invent. Math. 56 (1980), 117-128. |
[BP80b] | M. Broué and L. Puig, Characters and local structure in G-algebras, J. Algebra 63 (1980), 306-317. |
[Cr11] | D. A. Craven, The Theory of Fusion Systems: An Algebraic Approach, Cambridge University Press (2011). |
[Cr12] | D. A. Craven, Perverse Equivalences and Broué's Conjecture II: The Cyclic Case, arXiv:1207.0116 |
[CDR18] | D. A. Craven, O. Dudas and R. Rouquier, The Brauer trees of unipotent blocks, to appear, J. EMS, arXiv:1701.07097 |
[CEKL11] | D. A. Craven, C. W. Eaton, R. Kessar and M. Linckelmann, The structure of blocks with a Klein four defect group, Math. Z. 268 (2011), 441-476. |
[CG12] | D. A. Craven and A. Glesser, Fusion systems on small p-groups, Trans. AMS 364 (2012) 5945-5967. |
[CR13] | D. A. Craven and R. Rouquier, Perverse equivalences and Broué's conjecture, Adv. Math. 248 (2013), 1-58. |
[CuRe81a] | C. W. Curtis and I. Reiner, Methods of representation theory, with applications to finite groups and orders, Volume I, Wiley-Interscience (1981). |
[CuRe81b] | C. W. Curtis and I. Reiner, Methods of representation theory, with applications to finite groups and orders, Volume II, Wiley-Interscience (1981). |
[Da66] | E. C. Dade, Blocks with cyclic defect groups, Ann. Math. 84 (1966), 20-48. |
[DE20] | S. Danz and K. Erdmann, On Ext-Quivers of Blocks of weight two for symmetric groups, arXiv:2008.10999 |
[Du14] | O. Dudas, Coxeter orbits and Brauer trees II, Int. Math. Res. Not. 15 (2014), 4100-4123. |
[Dü04] | O. Düvel, On Donovan's conjecture, J. Algebra 272 (2004), 1-26. |
[Ea16] | C. W. Eaton, Morita equivalence classes of [math]2[/math]-blocks of defect three, Proc. AMS 144 (2016), 1961-1970. |
[Ea18] | C. W. Eaton, Morita equivalence classes of blocks with elementary abelian defect groups of order 16, arXiv:1612.03485 |
[EEL18] | C. W. Eaton, F. Eisele and M. Livesey, Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings, Math. Z. 295 (2020), 249-264. |
[EKKS14] | C. W. Eaton, R. Kessar, B. Külshammer and B. Sambale, [math]2[/math]-blocks with abelian defect groups, Adv. Math. 254 (2014), 706-735. |
[EKS12] | C. W. Eaton, B. Külshammer and B. Sambale, [math]2[/math]-blocks with minimal nonabelian defect groups, II, J. Group Theory 15 (2012), 311-321. |
[EL18a] | C. W. Eaton and M. Livesey, Classifying blocks with abelian defect groups of rank 3 for the prime 2, J. Algebra 515 (2018), 1-18. |
[EL18b] | C. W. Eaton and M. Livesey, Donovan's conjecture and blocks with abelian defect groups, Proc. AMS. 147 (2019), 963-970. |
[EL18c] | C. W. Eaton and M. Livesey, Some examples of Picard groups of blocks, J. Algebra 558 (2020), 350-370. |
[EL20] | C. W. Eaton and M. Livesey, Donovan's conjecture and extensions by the centralizer of a defect group arXiv:2006.11173 |
[Ei16] | F. Eisele, Blocks with a generalized quaternion defect group and three simple modules over a [math]2[/math]-adic ring, J. Algebra 456 (2016), 294-322. |
[Ei18] | F. Eisele, The Picard group of an order and Külshammer reduction, to appear, Algebr. Represent. Theory |
[Ei19] | F. Eisele, On the geometry of lattices and finiteness of Picard groups, arXiv:1908.00129 |
[EiLiv20] | F. Eisele and M. Livesey, Arbitrarily large Morita Frobenius numbers, arXiv:2006.13837 |
[Er82] | K. Erdmann, Blocks whose defect groups are Klein four groups: a correction, J. Algebra 76 (1982), 505-518. |
[Er87] | K. Erdmann, Algebras and dihedral defect groups, Proc. LMS 54 (1987), 88-114. |
[Er88a] | K. Erdmann, Algebras and quaternion defect groups, I, Math. Ann. 281 (1988), 545-560. |
[Er88b] | K. Erdmann, Algebras and quaternion defect groups, II, Math. Ann. 281 (1988), 561-582. |
[Er88c] | K. Erdmann, Algebras and semidihedral defect groups I, Proc. LMS 57 (1988), 109-150. |
[Er90] | K. Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Mathematics 1428, Springer-Verlag (1990). |
[Er90b] | K. Erdmann, Algebras and semidihedral defect groups II, Proc. LMS 60 (1990), 123-165. |
[Fa17] | N. Farrell, On the Morita Frobenius numbers of blocks of finite reductive groups, J. Algebra 471 (2017), 299-318. |
[FK18] | N. Farrell and R. Kessar, Rationality of blocks of quasi-simple finite groups, Represent. Theory 23 (2019), 325-349. |
[GO97] | H. Gollan and T. Okuyama, Derived equivalences for the smallest Janko group, preprint (1997). |
[GT19] | R. M. Guralnick and Pham Huu Tiep, Sectional rank and Cohomology, J. Algebra (2019) https://doi.org/10.1016/j.jalgebra.2019.04.023 |
[HK00] | G. Hiss and R. Kessar, Scopes reduction and Morita equivalence classes of blocks in finite classical groups, J. Algebra 230 (2000), 378-423. |
[HK05] | G. Hiss and R. Kessar, Scopes reduction and Morita equivalence classes of blocks in finite classical groups II, J. Algebra 283 (2005), 522-563. |
[Ho97] | T. Holm, Derived equivalent tame blocks, J. Algebra 194 (1997), 178-200. |
[HKL07] | T. Holm, R. Kessar and M. Linckelmann, Blocks with a quaternion defect group over a 2-adic ring: the case [math]\tilde{A}_4[/math], Glasgow Math. J. 49 (2007), 29–43. |
[Ja69] | G. Janusz, Indecomposable modules for finite groups, Ann. Math. 89 (1969), 209-241. |
[Jo96] | T. Jost, Morita equivalences for blocks of finite general linear groups, Manuscripta Math. 91 (1996), 121-144. |
[Ke96] | R. Kessar, Blocks and source algebras for the double covers of the symmetric and alternating groups, J. Algebra 186 (1996), 872-933. |
[Ke00] | R. Kessar, Equivalences for blocks of the Weyl groups, Proc. Amer. Math. Soc. 128 (2000), 337-346. |
[Ke01] | R. Kessar, Source algebra equivalences for blocks of finite general linear groups over a fixed field, Manuscripta Math. 104 (2001), 145-162. |
[Ke02] | R. Kessar, Scopes reduction for blocks of finite alternating groups, Quart. J. Math. 53 (2002), 443-454. |
[Ke05] | R. Kessar, A remark on Donovan's conjecture, Arch. Math (Basel) 82 (2005), 391-394. |
[KL18] | R. Kessar and M. Linckelmann, Descent of equivalences and character bijections, arXiv:1705.07227 |
[Ki84] | M. Kiyota, On 3-blocks with an elementary abelian defect group of order 9, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), 33–58. |
[Ko03] | S. Koshitani, Conjectures of Donovan and Puig for principal [math]3[/math]-blocks with abelian defect groups, Comm. Alg. 31 (2003), 2229-2243; Corrigendum, 32 (2004), 391-393. |
[KKW02] | S. Koshitani, N. Kunugi and K. Waki, Broué's conjecture for non-principal 3-blocks of finite groups, J. Pure and Applied Algebra 173 (2002), 177-211. |
[KKW04] | S. Koshitani, N. Kunugi and K. Waki, Broué's abelian defect group conjecture for Held group and the sporadic Suzuki group, J. Algebra 279 (2004), 638-666. |
[KoLa20] | S. Koshitani and C. Lassueur, Splendid Morita equivalences for principal 2-blocks with dihedral defect groups, Math. Z. 294 (2020), 639-666. |
[Kü80] | B. Külshammer, On 2-blocks with wreathed defect groups, J. Algebra 64 (1980), 529–555. |
[Kü81] | B. Külshammer, On p-blocks of p-solvable groups, Comm. Alg. 9 (1981), 1763-1785. |
[Kü91] | B. Külshammer, Group-theoretical descriptions of ring-theoretical invariants of group algebras, in Representation Theory of Finite Groups and Finite-Dimensional Algebras (Bielefeld, 1991), Progr. Math. 95, pp. 425-442, Birkhauser (1991). |
[Kü95] | B. Külshammer, Donovan's conjecture, crossed products and algebraic group actions, Israel J. Math. 92 (1995), 295-306. |
[KS13] | B. Külshammer and B. Sambale, The 2-blocks of defect 4, Representation Theory 17 (2013), 226-236. |
[Ku00] | N. Kunugi, Morita equivalent 3-blocks of the 3-dimensional projective special linear groups, Proc. LMS 80 (2000), 575-589. |
[Kup69] | H. Kupisch, Unzerlegbare Moduln endlicher Gruppen mit zyklischer p-Sylow Gruppe, Math. Z. 108 (1969), 77-104. |
[LM80] | P. Landrock and G. O. Michler, Principal 2-blocks of the simple groups of Ree type, Trans. AMS 260 (1980), 83-111. |
[Li94] | M. Linckelmann, The source algebras of blocks with a Klein four defect group, J. Algebra 167 (1994), 821-854. |
[Li94b] | M. Linckelmann, A derived equivalence for blocks with dihedral defect groups, J. Algebra 164 (1994), 244-255. |
[Li96] | M. Linckelmann, The isomorphism problem for cyclic blocks and their source algebras, Invent. Math. 125 (1996), 265-283. |
[Li18] | M. Linckelmann, The strong Frobenius numbers for cyclic defect blocks are equal to one, arXiv:1805.08884 |
[Li18b] | M. Linckelmann, Finite-dimensional algebras arising as blocks of ﬁnite group algebras, Contemporary Mathematics 705 (2018), 155-188. |
[Li18c] | M. Linckelmann, The block theory of finite group algebras, Volume 1, London Math. Soc. Student Texts 92, Cambridge University Press (2018). |
[Li18d] | M. Linckelmann, The block theory of finite group algebras, Volume 2, London Math. Soc. Student Texts 92, Cambridge University Press (2018). |
[LM20] | M. Linckelmann and W. Murphy, A 9-dimensional algebra which is not a block of a finite group, arXiv:2005.02223 |
[Liv19] | M. Livesey, On Picard groups of blocks with normal defect groups, arXiv:1907.12167 |
[LivM20] | M. Livesey and C. Marchi, On Picent for blocks with normal defect group, arXiv:2002.10571 |
[McK19] | E. McKernon, 2-Blocks whose defect group is homocyclic and whose inertial quotient contains a Singer cycle, arXiv:1912:03222 |
[MS08] | J. Müller and M. Schaps, The Broué conjecture for the faithful 3-blocks of [math]4.M_{22}[/math], J. Algebra 319 (2008), 3588-3602. |
[NS18] | G. Navarro and B. Sambale, On the blockwise modular isomorphism problem, Manuscripta Math. 157 (2018), 263-278. |
[Ne02] | G. Nebe, Group rings of finite groups over p-adic integers, some examples, Proceedings of the conference Around Group rings (Edmonton) Resenhas 5 (2002), 329-350. |
[Ok97] | T. Okuyama, Some examples of derived equivalent blocks of finite groups, preprint (1997). |
[Pu88] | L. Puig, Nilpotent blocks and their source algebras, Invent. Math. 93 (1988), 77-116. |
[Pu94] | L. Puig, On Joanna Scopes’ criterion of equivalence for blocks of symmetric groups, Algebra Colloq. 1 (1994), 25-55. |
[Pu99] | L. Puig, On the local structure of Morita and Rickard equivalences between Brauer blocks, Progress in Math. 178, Birkhauser Verlag (1999). |
[Pu09] | L. Puig, Block source algebras in p-solvable groups, Michigan Math. J. 58 (2009), 323-338. |
[Ri96] | J. Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. 72 (1996), 331-358. |
[Ro95] | R. Rouquier, From stable equivalences to Rickard equivalences for blocks with cyclic defect, Proceedings of Groups 1993, Galway-St. Andrews Conference, Vol. 2, London Math. Soc. Lecture Note Ser. 212, Cambridge University Press (1995), 512-523. |
[Ru11] | P. Ruengrot, Perfect isometry groups for blocks of finite groups, PhD Thesis, University of Manchester (2011). |
[Sa11] | B. Sambale, [math]2[/math]-blocks with minimal nonabelian defect groups, J. Algebra 337 (2011), 261–284. |
[Sa12] | B. Sambale, Blocks with defect group [math]D_{2^n} \times C_{2^m}[/math], J. Pure Appl. Algebra 216 (2012), 119–125. |
[Sa12b] | B. Sambale, Fusion systems on metacyclic 2-groups, Osaka J. Math. 49 (2012), 325–329. |
[Sa13] | B. Sambale, Blocks with defect group [math]Q_{2^n} \times C_{2^m}[/math] and [math]SD_{2^n} \times C_{2^m}[/math], Algebr. Represent. Theory 16 (2013), 1717–1732. |
[Sa13b] | B. Sambale, Blocks with central product defect group [math]D_{2^n} ∗ C_{2^m}[/math], Proc. Amer. Math. Soc. 141 (2013), 4057–4069. |
[Sa13c] | B. Sambale, Further evidence for conjectures in block theory, Algebra Number Theory 7 (2013), 2241–2273. |
[Sa14] | B. Sambale, Blocks of Finite Groups and Their Invariants, Lecture Notes in Mathematics, Springer (2014). |
[Sa16] | B. Sambale, 2-blocks with minimal nonabelian defect groups III, Pacific J. Math. 280 (2016), 475–487. |
[Sa20] | B. Sambale, Blocks with small-dimensional basic algebra arXiv:2005.13172 |
[SSS98] | M. Schaps, D. Shapira and O. Shlomo, Quivers of blocks with normal defect groups, Proc. Symp. in Pure Mathematics 63, Amer. Math. Soc. (1998), 497-510. |
[Sc91] | J. Scopes, Cartan matrices and Morita equivalence for blocks of the symmetric groups, J. Algebra 142 (1991), 441-455. |
[Sh20] | V. Shalotenko, Bounds on the dimension of Ext for finite groups, J. Algebra 550 (2020), 266-289. |
[St02] | R. Stancu, Almost all generalized extraspecial p-groups are resistant, J. Algebra 249 (2002), 120-126. |
[St06] | R. Stancu, Control of fusion in fusion systems, J. Algebra and its Applications 5 (2006), 817-837. |
[vdW91] | R. van der Waall, On p-nilpotent forcing groups, Indag. Mathem., N.S., 2 (1991), 367-384. |
[Wa00] | A. Watanabe, A remark on a splitting theorem for blocks with abelian defect groups, RIMS Kokyuroku 1140, Edited by H.Sasaki, Research Institute for Mathematical Sciences, Kyoto University (2000), 76-79. |
[WZZ18] | Chao Wu, Kun Zhang and Yuanyang Zhou, Blocks with defect group [math]Z_{2^n} \times Z_{2^n} \times Z_{2^m}[/math], J. Algebra 510 (2018), 469-498. |