Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality
The current article continues our project
on representation theory, Euler elements, causal homogeneous spaces and
Algebraic Quantum Field Theory (AQFT).
We call a pair (h,k) of Euler elements
orthogonal if $e^{πi \ad h} k = -k$.
We show that, if (h,k) and (k,h) are orthogonal, then
they generate a 3-dimensional simple subalgebra.
We also classify orthogonal Euler pairs in simple Lie algebras
and determine the fundamental groups of adjoint Euler elements
in arbitrary finite-di…
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