Grobner-Shirshov Bases for Replicated Algebras

被引：5
|
作者：
Kolesnikov, P. S. [1 ]
机构：
[1] Sobolev Inst Math, Akad Koptyug Prosp 4, Novosibirsk 630090, Russia
来源：
ALGEBRA COLLOQUIUM | 2017年 / 24卷 / 04期
关键词：
di-algebra; tri-algebra; Grobner-Shirshov basis; LEIBNIZ ALGEBRAS; DIAMOND LEMMA; DIALGEBRAS;
D O I：
10.1142/S1005386717000372
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner-Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincare-Birkhoff-Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD!-algebra).
引用
收藏
页码：563 / 576
页数：14
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