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

A class of mathematical dualities have played a central role in mapping states in gauge theory to states in the spacetime string theory dual. This includes the classical Schur-Weyl duality between symmetric groups and Unitary groups, as well as generalisations involving Brauer and Hecke algebras. The physical string dualities involved include examples from the AdS/CFT correspondence as well as ...

We discuss a previous attempt at a microscopic counting of the entropy of asymptot-ically flat non-extremal black-holes. This method used string dualities to relate 4 and 5 dimensional black holes to the BTZ black hole. We show how the dualities can be justified in a certain limit, equivalent to a near horizon limit, but the resulting spacetime is no longer asymptotically flat.