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The homology of the Temperley–Lieb algebras

Rachael Boyd and Richard Hepworth

Geometry & Topology 28 (2024) 1437–1499
Bibliography
1 A Björner, M Wachs, On lexicographically shellable posets, Trans. Amer. Math. Soc. 277 (1983) 323 MR0690055
2 C Bowman, A Cox, A Hazi, Path isomorphisms between quiver Hecke and diagrammatic Bott–Samelson endomorphism algebras, Adv. Math. 429 (2023) 109185 MR4611117
3 R Boyd, Homological stability for Artin monoids, Proc. Lond. Math. Soc. 121 (2020) 537 MR4100117
4 R Boyd, R Hepworth, Combinatorics of injective words for Temperley–Lieb algebras, J. Combin. Theory Ser. A 181 (2021) 105446 MR4235244
5 R Boyd, R Hepworth, P Patzt, The homology of the Brauer algebras, Selecta Math. 27 (2021) 85 MR4304560
6 J Brundan, A Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov–Lauda algebras, Invent. Math. 178 (2009) 451 MR2551762
7 R M Charney, Homology stability for GLn of a Dedekind domain, Invent. Math. 56 (1980) 1 MR0557579
8 T Church, Homological stability for configuration spaces of manifolds, Invent. Math. 188 (2012) 465 MR2909770
9 J Désarménien, Une autre interprétation du nombre de dérangements, Sém. Lothar. Combin. 8 (1983) 11
10 E Deutsch, L Shapiro, A survey of the Fine numbers, Discrete Math. 241 (2001) 241 MR1861421
11 C K Fan, R M Green, Monomials and Temperley–Lieb algebras, J. Algebra 190 (1997) 498 MR1441960
12 F D Farmer, Cellular homology for posets, Math. Japon. 23 (1979) 607 MR0529895
13 S Galatius, A Kupers, O Randal-Williams, Cellular Ek–algebras, preprint (2018) arXiv:1805.07184
14 J J Graham, G I Lehrer, Cellular algebras, Invent. Math. 123 (1996) 1 MR1376244
15 T Halverson, M Mazzocco, A Ram, Commuting families in Hecke and Temperley–Lieb algebras, Nagoya Math. J. 195 (2009) 125 MR2552957
16 J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR0786348
17 A Hatcher, N Wahl, Stabilization for mapping class groups of 3–manifolds, Duke Math. J. 155 (2010) 205 MR2736166
18 R Hepworth, Homological stability for families of Coxeter groups, Algebr. Geom. Topol. 16 (2016) 2779 MR3572348
19 R Hepworth, Homological stability for Iwahori–Hecke algebras, J. Topol. 15 (2022) 2174 MR4584588
20 V F R Jones, Index for subfactors, Invent. Math. 72 (1983) 1 MR0696688
21 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR0766964
22 W van der Kallen, Homology stability for linear groups, Invent. Math. 60 (1980) 269 MR0586429
23 C Kassel, V Turaev, Braid groups, 247, Springer (2008) MR2435235
24 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR0899057
25 L H Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990) 417 MR0958895
26 L H Kauffman, Knot diagrammatics, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 233 MR2179264
27 L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, 134, Princeton Univ. Press (1994) MR1280463
28 M C Kerz, The complex of words and Nakaoka stability, Homology Homotopy Appl. 7 (2005) 77 MR2155519
29 W B R Lickorish, Calculations with the Temperley–Lieb algebra, Comment. Math. Helv. 67 (1992) 571 MR1185809
30 H Maazen, Homology stability for the general linear group, PhD thesis, Utrecht University (1979)
31 M Nakaoka, Decomposition theorem for homology groups of symmetric groups, Ann. of Math. 71 (1960) 16 MR0112134
32 D Quillen, On the cohomology and K–theory of the general linear groups over a finite field, Ann. of Math. 96 (1972) 552 MR0315016
33 O Randal-Williams, Homological stability for unordered configuration spaces, Q. J. Math. 64 (2013) 303 MR3032101
34 O Randal-Williams, Resolutions of moduli spaces and homological stability, J. Eur. Math. Soc. 18 (2016) 1 MR3438379
35 O Randal-Williams, A remark on the homology of Temperley–Lieb algebras, preprint (2021)
36 D Ridout, Y Saint-Aubin, Standard modules, induction and the structure of the Temperley–Lieb algebra, Adv. Theor. Math. Phys. 18 (2014) 957 MR3281274
37 N J A Sloane, Jacobsthal sequence (or Jacobsthal numbers) : a(n) = a(n 1) + 2 a(n 2), with a(0) = 0, a(1) = 1 ; also a(n) = nearest integer to 2n3, from: "The on-line encyclopedia of integer sequences" (2000)
38 R Spencer, Jacobsthal elements, web resource (2022)
39 R A Spencer, The modular Temperley–Lieb algebra, Rocky Mountain J. Math. 53 (2023) 177 MR4585987
40 R J Sroka, The homology of a Temperley–Lieb algebra on an odd number of strands, (2022) arXiv:2202.08799
41 M Szymik, N Wahl, The homology of the Higman–Thompson groups, Invent. Math. 216 (2019) 445 MR3953508
42 H N V Temperley, E H Lieb, Relations between the “percolation” and “colouring” problem and other graph-theoretical problems associated with regular planar lattices : some exact results for the “percolation” problem, Proc. Roy. Soc. Lond. Ser. A 322 (1971) 251 MR0498284
43 B Webster, The existence of Jones–Wenzl projectors, (2017) MR3624396
44 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
45 H Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987) 5 MR0873400
46 B W Westbury, The representation theory of the Temperley–Lieb algebras, Math. Z. 219 (1995) 539 MR1343661