A Milnor-Moore Type Theorem for Braided Bialgebras
A Milnor-Moore Type Theorem for Braided Bialgebras
复制标题
辫状双代数的米尔诺-摩尔型定理
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
D. Ştefan
中科院分区：
文献类型：
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作者：
A. Ardizzoni;C. Menini;D. Ştefan
证明了连通辫子双代数无穷小余交换的Milnor-Moore定理。即在不同于2的特征上，证明了对于给定的连通辫子双代数$A$，对其基域中某个正则元素$\lambda\neq 0$有$\lambda$-余交换无穷小辫子，则$A$的无穷小辫子是标记$\lambda$的Hecke型的，并且$A$同构于它的本原元素辫子空间的对称代数.
The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra $A$ having a $\lambda $-cocommutative infinitesimal braiding for some regular element $\lambda \neq 0$ in the base field, then the infinitesimal braiding of $A$ is of Hecke-type of mark $\lambda$ and $A$ is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.