Department of Mathematics, Wayne State University, Detroit, MI 48202;
Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309; and.
Proc Natl Acad Sci U S A. 2014 Jul 8;111(27):9712-6. doi: 10.1073/pnas.1313078111. Epub 2014 Jun 30.
We identify a quantum lift of the greedy basis for rank 2 coefficient-free cluster algebras. Our main result is that our construction does not depend on the choice of initial cluster, that it builds all cluster monomials, and that it produces bar-invariant elements. We also present several conjectures related to this quantum greedy basis and the triangular basis of Berenstein and Zelevinsky.
我们为无系数 rank 2 系数簇代数的贪心基找到量子提升。我们的主要结果是我们的构造不依赖于初始簇的选择，它构建了所有的簇单项式，并且产生了不变元。我们还提出了几个与这个量子贪心基和 Berenstein 和 Zelevinsky 的三角基相关的猜想。
