刊名:Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
出版年:2017
出版时间:March 2017
年:2017
卷:58
期:1
页码:227-234
全文大小:
刊物类别:Mathematics and Statistics
刊物主题:Algebra; Geometry; Algebraic Geometry; Convex and Discrete Geometry;
出版者:Springer Berlin Heidelberg
ISSN:2191-0383
卷排序:58
文摘
Let \(\mathfrak {g}\) be the finite dimensional simple Lie algebra associated to an indecomposable and symmetrizable generalized Cartan matrix \(C=(a_{ij})_{n\times n}\) of finite type and let \(\mathfrak {d}\) be a finite dimensional Lie algebra related to a quantum group \(D_{q,p^{-1}}(\mathfrak {g})\) obtained by Hodges et al. (Adv Math 126:52–92, 1997) by deforming the quantum group \(U_q(\mathfrak {g})\). Here we see that \(\mathfrak {d}\) is a generalization of \(\mathfrak {g}\) and give a \(\mathfrak {d}\)-invariant symmetric bilinear form on \(\mathfrak {d}\).
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