Dirac structures and dynamical r-matrices

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 $\mathfrak{g}$, and prove that dynamical r-matrices are in one-one correspondence with certain Lagrangian subalgebras of $\mathfrak{g}\oplus \mathfrak{g}$.

LaTex, 21 pages