scholarly journals Support varieties for quantum groups

1998 ◽  
Vol 32 (4) ◽  
pp. 237-246 ◽  
Author(s):  
V. V. Ostrik
Keyword(s):  
Quantum Groups ◽  
Support Varieties

scholarly journals Support Varieties and Representation Type of Small Quantum Groups

2009 ◽  
Vol 2010 (7) ◽  
pp. 1346-1362 ◽  
Author(s):  
Jörg Feldvoss ◽  
Sarah Witherspoon
Keyword(s):  
Quantum Groups ◽  
Representation Type ◽  
Small Quantum ◽  
Support Varieties

Cohomology of Quantum Groups: the Quantum Dimension

1993 ◽  
Vol 45 (6) ◽  
pp. 1276-1298 ◽  
Author(s):  
Brian Parshall ◽  
Jian-Pan Wang
Keyword(s):  
Representation Theory ◽  
Quantum Groups ◽  
Elementary Theory ◽  
Root Of Unity ◽  
Support Varieties

AbstractThis paper uses the notion of the quantum dimension to obtain new results on the cohomology and representation theory of quantum groups at a root of unity. In particular, we consider the elementary theory of support varieties for quantum groups.

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 Support varieties for finite tensor categories: Complexity, realization, and connectedness

2021 ◽  
Vol 225 (9) ◽  
pp. 106705
Author(s):  
Petter Andreas Bergh ◽  
Julia Yael Plavnik ◽  
Sarah Witherspoon
Keyword(s):  
Tensor Categories ◽  
Support Varieties

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).

scholarly journals Bialgebra cohomology, deformations, and quantum groups.

1990 ◽  
Vol 87 (1) ◽  
pp. 478-481 ◽  
Author(s):  
M. Gerstenhaber ◽  
S. D. Schack
Keyword(s):  
Quantum Groups
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