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Dirac structures and dynamical r-matrices

Zhang-Ju Liu·Ping Xu
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Abstract

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 ${\frak g}\oplus \frak g$.

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Zhang-Ju Liu, Ping Xu. 1999-03-21. Dirac structures and dynamical r-matrices. https://arxiv.org/abs/math/9903119

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