3-Lie Bialgebras
Ruipu Bai, Jiaqian Li, Wei Meng
TL;DR
This paper introduces the concepts of 3-Lie coalgebras and bialgebras, explores their structures and relationships with 3-Lie algebras, and classifies 3-dimensional cases over algebraically closed fields.
Contribution
It defines 3-Lie coalgebras and bialgebras, studies their structures and relationships with 3-Lie algebras, and classifies low-dimensional instances.
Findings
Classification of 3-dimensional 3-Lie coalgebras
Classification of 3-dimensional 3-Lie bialgebras
Establishment of the structure theory for these algebras
Abstract
3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. The paper concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras, and the relationships with 3-Lie algebras are studied. And the classification of 3-dimensional 3-Lie coalgebras and 3-Lie bialgebras over an algebraically closed field of characteristic zero are provided.
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Taxonomy
TopicsAdvanced Topics in Algebra