E6(6) exceptional Drinfel'd algebras

The exceptional Drinfel'd algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel'd double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is E-6(6). We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold G, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel'd doubles and others that are not of this type.

Automated summary

The exceptional Drinfel'd algebra (EDA) is introduced as a Leibniz algebra to explore generalised notions of U-duality in M-theory. It provides an M-theoretic analogue of how a Drinfel'd double encodes generalised T-dualities of strings. The construction of the EDA, illustrated with examples, includes geometric realizations and natural generalizations of classical equations.