scholarly journals Some remarks on Koszul algebras and quantum groups

1987 ◽  
Vol 37 (4) ◽  
pp. 191-205 ◽  
Author(s):  
Yu. I. Manin
Keyword(s):  
Quantum Groups ◽  
Koszul 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).

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

Homogeneous Vector Bundles and Koszul Algebras

1998 ◽  
Vol 191 (1) ◽  
pp. 189-195 ◽  
Author(s):  
Lutz Hille
Keyword(s):  
Vector Bundles ◽  
Koszul Algebras ◽  
Homogeneous Vector

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

scholarly journals Remarks on the derived center of small quantum groups

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Anna Lachowska ◽  
You Qi
Keyword(s):  
Quantum Groups ◽  
Small Quantum
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