1999/03/19 by Zhangju Liu, Zhang-Ju Liu, Ping Xu +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.DG #math.QA
paper · pdf · doi:10.48550/arxiv.math/9903119
LaTex, 21 pages
openalex publication_date 1999/03/19 · arxiv created 1999/03/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to establish a connection between various subjects such as dynamical r-matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the theory of Dirac structures developed in dg-ga/9508013 and dg-ga/9611001. In particular, we give a new method of classifying dynamical r-matrices of simple Lie algebras \frak g, and prove that dynamical r-matrices are in one-one correspondence with certain Lagrangian subalgebras of \frak g⊕ \frak g.