Poisson triple systems

被引：0
|
作者：
Bremner, Murray R. [1 ]
Elgendy, Hader A. [2 ]
机构：
[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK, Canada
[2] Damietta Univ, Fac Sci, Dept Math, New Damietta, Egypt
来源：
LINEAR & MULTILINEAR ALGEBRA | 2023年 / 71卷 / 07期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Poisson algebras; Poisson triple systems; universal enveloping algebras; algebraic operads; Koszul operads; computer algebra; ALGEBRAS;
D O I：
10.1080/03081087.2022.2053039
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system has a universal enveloping Poisson algebra. Finally, we briefly discuss operadic aspects of Poisson triple systems.
引用
收藏
页码：1145 / 1157
页数：13
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