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Poincaré-Birkhoff-Witt Basis
- 刊名:Lecture Notes in Mathematics
- 出版年:2015
- 出版时间:2015
- 年:2015
- 卷:2150
- 期:1
- 页码:71-97
- 全文大小:350 KB
- 参考文献:1.Abe, E.: Hopf Algebras. Cambridge University Press, Cambridge (1980)MATH
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- 作者单位:Vladislav Kharchenko (14)
14. Universidad Nacional Autónoma de México, Cuautitlán Izcalli, Estado de México, Mexico
- 丛书名:Quantum Lie Theory
- ISBN:978-3-319-22704-7
- 刊物类别:Mathematics and Statistics
- 刊物主题:Mathematics
Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Mathematical Biology Partial Differential Equations Functional Analysis Abstract Harmonic Analysis Group Theory and Generalizations
- 出版者:Springer Berlin / Heidelberg
- ISSN:1617-9692
文摘
In this chapter, we demonstrate that every character Hopf algebra has a PBW basis. A Hopf algebra H is referred to as a character Hopf algebra if the group G of all group-like elements is commutative and H is generated over k [G] by skew-primitive semi-invariants, whereas a well-ordered subset \(V \subseteq H\) is a set of PBW generators of H if there exists a function \(h: V \rightarrow \mathbf{Z^{+}} \cup \{\infty \},\) called the height function, such that the set of all products $$\displaystyle{gv_{1}^{n_{1} }v_{2}^{n_{2} }\,\cdots \,v_{k}^{n_{k} },}$$ where \(g \in G,\ \ v_{1} < v_{2} <\ldots < v_{k} \in V,\ \ n_{i} < h(v_{i}),1 \leq i \leq k\) is a basis of H. 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