GROBNER-SHIRSHOV BASES FOR DIALGEBRAS

被引：43

作者：

Bokut, L. A. ^{[1
,2
]}

Chen, Yuqun ^{[1
]}

Liu, Cihua ^{[1
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2010年 / 20卷 / 03期

关键词：

Dialgebra; Grobner-Shirshov basis; Leibniz algebra; Clifford dialgebra; ALGEBRAS;

D O I：

10.1142/S0218196710005753

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we define the Grobner-Shirshov basis for a dialgebra. The Composition-Diamond lemma for dialgebras is given then. As a result, we give Grobner-Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.

引用

页码：391 / 415

页数：25

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