科研之友
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摘要
For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra (U) over dot and its canonical basis (B) over dot given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set (M) over tilde which depends only on the root category R and prove that there is a bijection between (M) over tilde and. B, where R is the T-2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U+.
