GROBNER-SHIRSHOV BASES FOR ROTA-BAXTER ALGEBRAS

被引：30

作者：

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

Chen, Yu. ^{[1
]}

Deng, X. ^{[1
]}

机构：

[1] S China Normal Univ, Guangzhou, Guangdong, Peoples R China

[2] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2010年 / 51卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

Rota-Baxter algebra; Grobner-Shirshov basis; COMPOSITION-DIAMOND LEMMA; FIELD; RENORMALIZATION; SINGULARITIES; RESOLUTION; VARIETY;

D O I：

10.1007/s11202-010-0097-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the composition-diamond lemma for associative nonunitary Rota-Baxter algebras of weight lambda. To give an application, we construct a linear basis for a free commutative and nonunitary Rota-Baxter algebra, show that every countably generated Rota-Baxter algebra of weight 0 can be embedded into a two-generated Rota-Baxter algebra, and prove the 1/2-PBW theorems for dendriform dialgebras and trialgebras.

引用

页码：978 / 988

页数：11

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