Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras
Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras
复制标题
泛包络代数和对合 Hom-Lie 代数的 Poincaré-Birkhoff-Witt 定理
作者：
郭锂;张斌;郑上华
homtype代数，特别是homlie代数，已经引起了广泛的关注。近年来备受关注。一个homlie代数被称为对合代数，如果它的hom映射是。乘法和对合。在本文中，我们得到了自由的显式构造。在hm -模上的对合hm -结合代数。然后我们应用这个结构。得到对合homlie代数的全称包络代数。最后我们。的包络代数推广了著名的庞加莱-比克霍-维特定理。李代数到对合的homlie -Lie代数。
Hom-type algebras, in particular Hom-Lie algebras, have attracted quite.much attention in recent years. A Hom-Lie algebra is called involutive if its Hom map is.multiplicative and involutive. In this paper, we obtain an explicit construction of the free.involutive Hom-associative algebra on a Hom-module. We then apply this construction.to obtain the universal enveloping algebra of an involutive Hom-Lie algebra. Finally we.generalize the well-known Poincar´e-Birkho-Witt theorem for enveloping algebras of.Lie algebras to involutive Hom-Lie algebras.