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- W2952551566 abstract "For symmetrizable Kac-Moody Lie algebra $textbf{g}$, Lusztig introduced the modified quantized enveloping algebra $dot{textbf{U}}(textbf{g})$ and its canonical basis in [12]. In this paper, for finite and affine type symmetric Lie algebra $textbf{g}$ we define a set which depend only on the root category and prove that there is a bijection between the set and the canonical basis of $dot{textbf{U}}(textbf{g})$, where the root category is the $T^2$-orbit category of the derived category of Dynkin or tame quiver. Our method bases on one theorem of Lin, Xiao and Zhang in [9], which gave the PBW-basis of $textbf{U}^+(textbf{g})$." @default.
- W2952551566 created "2019-06-27" @default.
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- W2952551566 date "2012-10-23" @default.
- W2952551566 modified "2023-10-14" @default.
- W2952551566 title "A parameterization of the canonical bases of affine modified quantized enveloping algebras" @default.
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- W2952551566 doi "https://doi.org/10.48550/arxiv.1210.6129" @default.
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