Trace Decategorification of Categorified Quantum sl(3)
Trace Decategorification of Categorified Quantum sl(3)
复制标题
分类量子 sl(3) 的迹去分类
DOI：
10.1007/s10485-022-09704-x
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发表时间：
2014
影响因子：
0.6
通讯作者：
M. Živković
中科院分区：
文献类型：
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作者：
M. Živković
我们证明了Khovanov和Lauda引入的范畴化量子$$\mathfrak{sl}_3$$sl 3的迹也可以被量子$$\mathfrak{sl}_3$$sl 3所标识，从而提供了一种非范畴化的另一种方法。这是量子$$\mathfrak{sl}_n$$sl n群在整数上的迹非范畴化的第二步，第一步是$$\mathfrak{sl}_2$$sl 2情形。所使用的主要技术是将归类量子群解耦为其正和负部分。这一方法可用于更一般的范畴化量子群，将问题归结为其正部分的迹非范畴化。在量子$$\mathfrak{sl}_3$$sl 3的情况下，基于StošIć找到的不可分解部分，它的正(同构为负)部分的标准基有一个显式的形式，从而得到了在这种情况下的全部结果。
We prove that the trace of categorified quantum $$\mathfrak {sl}_3$$ sl 3 introduced by Khovanov and Lauda can also be identified with quantum $$\mathfrak {sl}_3$$ sl 3 , thus providing an alternative way of decategorification. This is the second step of trace decategorification of quantum $$\mathfrak {sl}_n$$ sl n groups over the integers, the first being the $$\mathfrak {sl}_2$$ sl 2 case. The main technique used is decoupling of categorified quantum group into its positive and negative part. This technique can be used for more general categorified quantum groups to reduce the problem to the trace decategorification of its positive part. In the case of quantum $$\mathfrak {sl}_3$$ sl 3 , there is an explicit form of the canonical basis of the positive (and isomorphically negative) part of it based on indecomposables found by Stošić, leading to the full result in this case.