A Grassmann and graded approach to coboundary Lie bialgebras, their classification, and Yang-Baxter equations

2017/10/13 by de Lucas, J., D. Wysocki, Wysocki, D.
Mathematics · #17B40 (secondary) #17B62 (primary) 17B22 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1710.05022

openalex publication_date 2017/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work pioneers the systematic study and classification (up to Lie algebra automorphisms) of finite-dimensional coboundary Lie bialgebras through Grassmann algebras. Several mathematical structures on Lie algebras, e.g. Killing forms or root decompositions, are extended to the Grassmann algebras of Lie algebras. This simplifies the description of the procedures and tools appearing in the theory of Lie bialgebras and originates novel techniques for its study and classification up to Lie algebra automorphisms. As a particular case, the classification of real three-dimensional coboundary Lie bialgebras is retrieved.

Citations

• Theory of Group Representations and Applications

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