量子仿射代数Uq(sln)的范畴化

The Categorification of Quantum Affine Algebra U_q(sl_n)

用弦图构造了与Lusztig的量子群U=U_q(sl_n)对应的2-范畴u和u.其中u是u的Karoubi包络.通过构造u的2-表示,可以证明u的Grothendieck环K_0(u)同构于代数_AU,其中U是U的幂等变形,而_AU是U的整形式.由此得到的范畴u就是量子仿射代数U_q(sl_n)的范畴化.

We construct 2-categories uand 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 Lt, we also prove that the Grothendieck ring K0（U） ofU is isomorphic to the algebra U, where U is the idempotented modification of U and U is the integral form of l）. We obtain that the category U could be considered as the categorification of quantum affine algebra Uq（sln）.