Majid conjecture:quantum Kac-Moody algebras version
Majid conjecture:quantum Kac-Moody algebras version
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马吉德猜想：量子 Kac-Moody 代数版本
DOI：
10.1007/s11464-021-0905-x
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发表时间：
2021
影响因子：
--
通讯作者：
Xia Limeng
中科院分区：
文献类型：
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作者：
Hu Hongmei;Hu Naihong;Xia Limeng
基于广义双玻色化构造的n重张量积形式，证明了量子Kac-Moody代数形式的Majid猜想。特别地，我们明确给出了仿射型，，和Tp，q，r的量子Kac-Moody代数的双玻色化型交叉构造，从而在相关的辫张量范畴中恢复了具有R-矩阵定义的辫群的量子Kac-Moody代数的生成元.这使我们更好地理解量子Kac-Moody代数作为模代数/模余代数关于其内部有限型量子子代数的某种扩张的代数结构本身。
Based on then-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types,, andTp,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined byR-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.