scholarly journals Drinfeld Realization of Quantum Twisted Affine Algebras via Braid Group

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Naihuan Jing ◽  
Honglian Zhang
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Previous Approach ◽  
Quantum Affine Algebras ◽  
Conceptual Proof ◽  
Affine Algebras ◽  
Braid Group Action

The Drinfeld realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig’s braid group action.

scholarly journals TRIPLY-GRADED LINK HOMOLOGY AND HOCHSCHILD HOMOLOGY OF SOERGEL BIMODULES

2007 ◽  
Vol 18 (08) ◽  
pp. 869-885 ◽  
Author(s):  
MIKHAIL KHOVANOV
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Polynomial Algebra ◽  
Homology Theory ◽  
Hochschild Homology ◽  
Polynomial Algebras ◽  
Homology Groups ◽  
Link Homology ◽  
Soergel Bimodules ◽  
Braid Group Action

We consider a class of bimodules over polynomial algebras which were originally introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct summand of the category of Harish–Chandra modules for sl(n). Rouquier used Soergel bimodules to construct a braid group action on the homotopy category of complexes of modules over a polynomial algebra. We apply Hochschild homology to Rouquier's complexes and produce triply-graded homology groups associated to a braid. These groups turn out to be isomorphic to the groups previously defined by Lev Rozansky and the author, which depend, up to isomorphism and overall shift, only on the closure of the braid. Consequently, our construction produces a homology theory for links.

scholarly journals Braid Group Action and Canonical Bases

1996 ◽  
Vol 122 (2) ◽  
pp. 237-261 ◽  
Author(s):  
George Lusztig
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Canonical Bases ◽  
Braid Group Action

scholarly journals A BRAIDED SIMPLICIAL GROUP

2002 ◽  
Vol 84 (3) ◽  
pp. 645-662 ◽  
Author(s):  
JIE WU
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Homotopy Group ◽  
Braid Groups ◽  
Subject Classification ◽  
Homotopy Groups ◽  
Simplicial Group ◽  
Pure Braid Group ◽  
Fixed Set ◽  
Braid Group Action

By studying the braid group action on Milnor's construction of the 1-sphere, we show that the general higher homotopy group of the 3-sphere is the fixed set of the pure braid group action on certain combinatorially described groups. This establishes a relation between the braid groups and the homotopy groups of the sphere.2000Mathematical Subject Classification: 20F36, 55P35, 55Q05, 55Q40, 55U10.

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