Pointed irreducible bialgebras
Pointed irreducible bialgebras
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尖不可约双代数
DOI：
10.1016/0021-8693(79)90208-4
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发表时间：
1979
影响因子：
0.9
通讯作者：
Warren D. Nichols
中科院分区：
文献类型：
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作者：
Warren D. Nichols
这是众所周知的[5，第274页，定理13.0]。11在特征为零的域上的一个点不可约协交换双代数B与B的基元的李代数P (B)的全称包络代数U （P （B)）同构，一种证明方法是首先证明B和U@ ' (B)）与向量空间P (B)上的无协不可约的点不可约协交换双代数同构，然后利用这些协代数同构推导出一个双代数同构。在本文中，我们证明了上述的一个对偶版本。设B是特征为0的域上的一个点不可约交换双代数。I表示增广理想，Q (B)= l/r2。那么B作为双代数同构于适当的通用对象UIC （Q (B)）。我们首先证明了每一个代数对于Sym （Q (B)）都是同构的，然后利用这些代数同构推导出一个双代数同构。
It is well-known [5, p. 274, Theorem 13.0. 11 that a pointed irreducible cocommutative bialgebra B over a field of characteristic zero is isomorphic as a bialgebra to U (P (B)), the universal enveloping algebra of the Lie algebra P (B) of primitives of B. One method of proof is first to show that B and U@‘(B)) are each coalgebra-isomorphic to the cofree pointed irreducible cocommutative coalgebra on the vector space P (B), and then to use these coalgebra isomorphisms to induce a bialgebra isomorphism.In this paper we prove a dual version of the above. Let B be a pointed irreducible commutative bialgebra over a field of characteristic zero. Write I for its augmentation ideal, and Q (B)= l/r2. Then B is isomorphic as a bialgebra to the appropriate universal object UIC (Q (B)). We first show that each is isomorphic as an algebra to Sym (Q (B)), and then use these algebra isomorphisms to induce a bialgebra isomorphism.