分类量子群的晶体
The crystal of the categorified quantum group
- Seoul National University（首尔大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文通过无有限性条件的阿贝尔范畴上的范畴作用构造晶体，实现修正量子包络代数晶体的分类化，并识别Webster张量积晶体，进而分类化极值权模。
中文摘要 AI 辅助
本文给出了与对称化Kac-Moody代数$\mathfrak{g}$相关的修正量子包络代数的晶体$B(\widetilde{U}_q(\mathfrak{g}))$的一个分类化。从无有限性条件的阿贝尔范畴上的范畴$\mathfrak{g}$作用构造了一个晶体，并利用该晶体构造了分类量子群的自对偶不可分解对象集合上的双晶体结构。Webster的广义张量积分类化中的晶体被识别为最低权和最高权晶体的张量积。作为应用，获得了极值权模的一个分类化。
英文摘要
A categorification of the crystal $B(\widetilde{U}_q(\mathfrak{g}))$ of the modified quantized enveloping algebra associated to a symmetrizable Kac-Moody algebra $\mathfrak{g}$ is given. A crystal is constructed from a categorical $\mathfrak{g}$-action on abelian categories without finiteness conditions, and is used to construct the bicrystal structure on the set of self-dual indecomposable objects of the categorified quantum group. Crystals from Webster's generalized tensor product categorification are identified with tensor products of lowest and highest weight crystals. As an application, a categorification of the extremal weight module is obtained.
