Algebras, hyperalgebras, nonassociative bialgebras and loops
Algebras, hyperalgebras, nonassociative bialgebras and loops
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DOI：
10.1016/j.aim.2006.04.001
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发表时间：
2007-01
影响因子：
1.7
通讯作者：
J. M. Pérez-Izquierdo
中科院分区：
文献类型：
--
作者：
J. M. Pérez-Izquierdo
Sabinin代数是李代数的广义推广，包括李代数，Malcev代数和Bol代数作为非常特殊的例子。给出了Sabinin代数的一个泛包络代数的构造，以及相应的Poincaré-Birkhoff-Witt定理.本文还介绍了Hopf代数的一个非结合对应，并证明了Milnor-Moore定理的一个版本。Sabinin代数的Loop代数和泛包络代数是这些非结合Hopf代数的自然例子。回路的恒等式通过线性化过程转化为非结合Hopf代数的恒等式。这样，非结合代数和Hopf代数就平滑地交织在一起。
Sabinin algebras are a broad generalization of Lie algebras that include Lie, Malcev and Bol algebras as very particular examples. We present a construction of a universal enveloping algebra for Sabinin algebras, and the corresponding Poincaré–Birkhoff–Witt Theorem. A nonassociative counterpart of Hopf algebras is also introduced and a version of the Milnor–Moore Theorem is proved. Loop algebras and universal enveloping algebras of Sabinin algebras are natural examples of these nonassociative Hopf algebras. Identities of loops move to identities of nonassociative Hopf algebras by a linearizing process. In this way, nonassociative algebras and Hopf algebras interlace smoothly.