Half-maximal extended Drinfel'd algebras.

The extended Drinfel'd algebra (ExDA) is the underlying symmetry of non-Abelian duality in the low-energy effective theory of string theory. Non-Abelian U -dualities in maximal supergravities have been studied well, but there has been no study on non-Abelian dualities in half-maximal supergravities. We construct the ExDA for half-maximal supergravities in d ≥ 4. We also find an extension of the homogeneous classical Yang–Baxter equation in these theories. [ABSTRACT FROM AUTHOR]