Framing the exceptional lie group G2

On the topology of the exceptional Lie group G 2

Intrinsic formulae for the Casimir operators of semidirect products of the exceptional Lie algebra G2 and a Heisenberg Lie algebra

We show that the Casimir operators of the semidirect products G2 ⊕2Γ(a,b)⊕Γ(0,0)h of the exceptional Lie algebra G2 and a Heisenberg algebra h can be constructed explicitly from the Casimir operators of G2.

GROUP THEORY Exceptional Lie groups as invariance groups

We offer the ultimate birdtracker guide to exceptional Lie groups.

Exceptional Lie groups

Now, in the present book, we describe simply connected compact exceptional simple Lie groups G2, F4, E6, E7, E8, in very elementary way. The contents are given as follows. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms σ of G, and determine the group structures of the fixed points subgroup G by σ. Note that they co...

On Lie induction and the exceptional series

Lie bialgebras occur as the principal objects in the infinitesimalisation of the theory of quantum groups—the semi-classical theory. Their relationship with the quantum theory has made available some new tools that we can apply to classical questions. In this paper, we study the simple complex Lie algebras using the double-bosonisation construction of Majid. This construction expresses algebrai...