Quantum Groups, Hall Algebras and Quantized Shuffles

1997 ◽  
pp. 273-290 ◽  
Author(s):  
James A. Green
Keyword(s):  
Quantum Groups ◽  
Hall Algebras

scholarly journals Cohomological Hall algebras and affine quantum groups

2017 ◽  
Vol 24 (2) ◽  
pp. 1093-1119 ◽  
Author(s):  
Yaping Yang ◽  
Gufang Zhao
Keyword(s):  
Quantum Groups ◽  
Hall Algebras

scholarly journals Quantum groups via Hall algebras of complexes

2013 ◽  
Vol 177 (2) ◽  
pp. 739-759 ◽  
Author(s):  
Tom Bridgeland
Keyword(s):  
Quantum Groups ◽  
Hall Algebras

Hall algebras, hereditary algebras and quantum groups

1995 ◽  
Vol 120 (1) ◽  
pp. 361-377 ◽  
Author(s):  
James A. Green
Keyword(s):  
Quantum Groups ◽  
Hall Algebras ◽  
Hereditary Algebras

scholarly journals K-theoretic Hall algebras, quantum groups and super quantum groups

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
M. Varagnolo ◽  
E. Vasserot
Keyword(s):  
Quantum Groups ◽  
Hall Algebras

scholarly journals Hall algebras and quantum groups

1990 ◽  
Vol 101 (1) ◽  
pp. 583-591 ◽  
Author(s):  
Claus Michael Ringel
Keyword(s):  
Quantum Groups ◽  
Hall Algebras

scholarly journals On cocycle twisting of compact quantum groups

2010 ◽  
Vol 258 (10) ◽  
pp. 3362-3375 ◽  
Author(s):  
Kenny De Commer
Keyword(s):  
Quantum Groups ◽  
Compact Quantum Groups

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

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