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- Title
Quantized GIM Algebras and their Images in Quantized Kac-Moody Algebras.
- Authors
Gao, Yun; Hu, Naihong; Xia, Li-meng
- Abstract
For any simply-laced GIM Lie algebra L , we present the definition of quantum universal enveloping algebra U q (L) , and prove that there is a quantum universal enveloping algebra U q (A) of an associated Kac-Moody algebra A , together with an involution (ℚ -linear) σ, such that U q (L) is isomorphic to the ℚ (q) -extension S ~ q of the σ-involutory subalgebra Sq of U q (A) . This result gives a quantum version of Berman's work (Berman Comm. Algebra 17, 3165–3185, 1989) in the simply-laced cases. Finally, we describe an automorphism group of U q (L) consisting of Lusztig symmetries as a braid group.
- Publication
Algebras & Representation Theory, 2021, Vol 24, Issue 3, p565
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1007/s10468-020-09960-2