Oeh D (2023)
Publication Type: Journal article
Publication year: 2023
Book Volume: 217
Journal Issue: 3
DOI: 10.1007/s10711-023-00785-z
Let g be a real finite-dimensional Lie algebra containing pointed generating invariant closed convex cones. We determine those derivations D of g which induce a 3-grading of the form g = g-1 circle plus g(0) circle plus g1 on g such that the (+/- 1)-eigenspaces g +/- 1 of D are generated by the intersections with generating cones of the form W = O-f(& lowast;), where O f is the coadjoint orbit of a linear functional f is an element of z(g)(& lowast;) and O-f(& lowast;) is the dual cone of O-f. In particular, we show that, if g is solvable, no such derivation except the trivial one exists.This continues our classification of Lie algebras generated by Lie wedges of endomorphism semigroups of standard subspaces. The classification is motivated by the relation of nets of standard subspaces to Haag-Kastler nets of von Neumann algebras in Algebraic Quantum Field Theory.
APA:
Oeh, D. (2023). Three-gradings of non-reductive admissible Lie algebras induced by derivations. Geometriae Dedicata, 217(3). https://dx.doi.org/10.1007/s10711-023-00785-z
MLA:
Oeh, Daniel. "Three-gradings of non-reductive admissible Lie algebras induced by derivations." Geometriae Dedicata 217.3 (2023).
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