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Rindler wedges are fundamental localization regions in AQFT. They aredetermined by the one-parameter group of boost symmetries fixing the wedge. Thealgebraic canonical construction of the free field provided byBrunetti-Guido-Longo (BGL) arises from the wedge-boost identification, the BWproperty and the PCT Theorem.  In this paper we generalize this picture in the following way. Firstly, givena $\mathbb Z_2$-graded Lie group we define a (twisted-)local poset of abstractwedge regions. We classify (semisimple) Lie algebras supporting abstract wedgesand study special wedge configurations. This allows us to exhibit an analog ofthe Haag-Kastler one-particle net axioms for such general Lie groups withoutreferring to any specific spacetime. This set of axioms supports a firstquantization net obtained by generalizing the BGL construction. Theconstruction is possible for a large family of Lie groups and provides severalnew models. We further comment on orthogonal wedges and extension ofsymmetries.

Covariant homogeneous nets of standard subspaces