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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.19632 |
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Table of Contents:
- Let $\mathfrak{g}$ be a simple Lie algebra over~$\mathbb{C}$ with root system~$Φ$. In the simply laced case, Frenkel and Kac found a particularly simple construction of~$\mathfrak{g}$, together with a Chevalley basis and explicitly given structure constants, in terms of a certain multiplicative $2$-cocycle $\varepsilon\colon \mathbb{Z} Φ\times \mathbb{Z}Φ\rightarrow\{\pm 1\}$. We show that Lusztig's canonical basis of~$\mathfrak{g}$ can also be obtained in this way, for a suitable choice of~$\varepsilon$. We also address the problem of explicitly describing the structure constants when $Φ$ is not simply laced.