Gr\"obner-Shirshov bases and their calculation
L.A. Bokut, Yuqun Chen
TL;DR
This survey introduces the theory of Gr"obner-Shirshov bases for associative and Lie algebras, including new lemmas and applications, providing a comprehensive overview of their calculation methods.
Contribution
It formulates the Gr"obner-Shirshov bases theory for associative and Lie algebras and presents new Composition-Diamond lemmas and applications.
Findings
New Composition-Diamond lemmas introduced
Framework for calculating Gr"obner-Shirshov bases established
Applications in algebraic structures discussed
Abstract
In this survey, we formulate the Gr\"{o}bner-Shirshov bases theory for associative algebras and Lie algebras. Some new Composition-Diamond lemmas and applications are mentioned.
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