论文标题
Gröbner-Shirshov基础理论和Leibniz Superalgebras的扩展
Gröbner-Shirshov bases theory and extensions of Leibniz superalgebras
论文作者
论文摘要
在本文中，我们详细介绍了莱布尼兹（Super）代数的Gröbner-Shirshov方法。我们表明，对于自由莱布尼兹（超级）代数的每个（分级）理想，有独特的减少Gröbner-Shirshov的基础。作为应用，我们构建了自由metabelian leibniz超级甲虫的线性底座和自由metabelian lie代数的新线性基础。我们介绍了另一个莱布尼兹（Super）代数的莱布尼兹（超级）代数扩展的完整表征，其中前者由发电机和关系提出。
In this paper, we elaborate Gröbner-Shirshov bases method for Leibniz (super)algebras. We show that there is a unique reduced Gröbner-Shirshov basis for every (graded) ideal of a free Leibniz (super)algebra. As applications, we construct linear bases of free metabelian Leibniz superalgebras and new linear bases of free metabelian Lie algebras. We present a complete characterization of extensions of a Leibniz (super)algebra by another Leibniz (super)algebra, where the former is presented by generators and relations.
