\dot{U}^+_3的不可分解1-态射与U_q^+（sl_3）的标准基
Indecomposable 1-morphisms of \dot{U}^+_3 and the canonical basis of U_q^+(sl_3)
摘要：
我们计算了\dot{U}^+_3的不可分解对象-这个范畴将量子s1_3的正半部分归类，并且我们将任意对象分解为不可分解的对象。在非范畴化的水平上，我们得到了量子sl_3的正半部分U^+_q（sl_3）的Lusztig正则基.通过在$\dot{U}^+_3$的同伦范畴中定义一个同伦为零的复形，我们还对U_q^+（sl_3）中的高量子塞尔关系进行了分类。我们使用定义在整数环上的范畴$\dot{U}^+_3$。本文基于引入的（扩展的）图解演算对量子群进行分类。
英文摘要：
We compute the indecomposable objects of \dot{U}^+_3 - the category that categorifies the positive half of the quantum sl_3, and we decompose an arbitrary object into indecomposable ones. On decategorified level we obtain the Lusztig's canonical basis of the positive half U^+_q(sl_3) of the quantum sl_3. We also categorify the higher quantum Serre relations in U_q^+(sl_3), by defining a certain complex in the homotopy category of $\dot{U}^+_3$ that is homotopic to zero. We work with the category $\dot{U}^+_3$ that is defined over the ring of integers. This paper is based on the (extended) diagrammatic calculus introduced to categorify quantum groups.
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