Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (3): 431-465.

• Articles • Previous Articles     Next Articles

The Categorification of Quantum Affine Algebra Uq(sln)

 REN Lei, CHANG Wen-Jing, WANG Na, WANG Zhi-Xi, WU Ke, YANG Zi-Feng   

  1. School of Mathematical Science, Capital Normal University, Beijing 100048
  • Received:2011-10-23 Revised:2013-02-01 Online:2013-06-25 Published:2013-06-25
  • Supported by:

    国家自然科学基金(10975102, 11031005, 10871135, 10871227)和 北京市创新团队项目(201007107) 资助

Abstract:

We construct 2-categories U and U using string diagrams corresponding to Lusztig's quantum group U=Uq(sln). Here U is the Karoubi envelope of U. By constructing the 2-representation of U, we also prove that the Grothendieck ring K0(U) of U is isomorphic to the algebra AU, where U is the idempotented modification of U and AU is the integral form of U. We obtain that the category U could be considered as the categorification of quantum affine algebra Uq(sln).

Key words: Quantum affine algebra, Categorification, 2-representation

CLC Number: 

  • 81R10
Trendmd