Drinfeld type presentations of loop algebras
Drinfeld type presentations of loop algebras
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循环代数的 Drinfeld 型表示
DOI：
10.1090/tran/8120
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发表时间：
2020
影响因子：
1.3
通讯作者：
Shaobin Tan
中科院分区：
文献类型：
--
作者：
Fulin Chen;Naihuan Jing;Fei Kong;Shaobin Tan
设为有限型或仿射型Kac-Moody李代数的导子代数，设为的图自同构，设为的圈代数。本文利用顶点代数技巧，给出了图的泛中心扩张的电流型表示的一般构造。建设包含经典极限德林费尔德的新实现（扭曲和untwisted）量子仿射代数[苏联数学。36（1988），pp. 212-216]和环形李代数的Moody-Rao-Yokonuma表示[Geom. Dedicata 35（1990），pp. 283-307]作为特殊例子。作为应用，当是simply-laced-type时，我们证明了[J. Math. Phys. 59（2018），081701]中引入的量子Kac-Moody代数的-扭曲量子仿射的经典极限是的泛包络代数。引用
Letbe the derived subalgebra of a Kac-Moody Lie algebra of finite-type or affine-type, letbe a diagram automorphism of, and letbe the loop algebra ofassociated to. In this paper, by using the vertex algebra technique, we provide a general construction of current-type presentations for the universal central extensionof. The construction contains the classical limit of Drinfeld’s new realization for (twisted and untwisted) quantum affine algebras [Soviet Math. Dokl. 36 (1988), pp. 212–216] and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras [Geom. Dedicata 35 (1990), pp. 283–307] as special examples. As an application, whenis of simply-laced-type, we prove that the classical limit of the-twisted quantum affinization of the quantum Kac-Moody algebra associated tointroduced in [J. Math. Phys. 59 (2018), 081701] is the universal enveloping algebra of. References