Oeh D (2021)
Publication Type: Journal article
Publication year: 2021
DOI: 10.1007/s00031-020-09635-8
Let (g, tau) be a real simple symmetric Lie algebra and let W subset of g be an invariant closed convex cone which is pointed and generating with tau(W) = -W. For elements h is an element of g with tau(h) = h, we classify the Lie algebras g (W, tau, h) which are generated by the closed convex cones C +/- (W, tau, h) := (+/- W) boolean AND g(+/- 1)(-tau) (h), where g(+/- 1)(-tau) := {x is an element of g : tau(x) - x [h, x] - +/- x}. These cones occur naturally as the skew-symmetric parts of the Lie wedges of endomorphism semigroups of certain standard subspaces. We prove in particular that, if g (W, tau, h) is non-trivial, then it is either a hermitian simple Lie algebra of tube type or a direct sum of two Lie algebras of this type. Moreover, we give for each hermitian simple Lie algebra and each equivalence class of involutive automorphisms tau of g with tau(W) = -W a list of possible subalgebras g(W, tau, h) up to isomorphy.
APA:
Oeh, D. (2021). CLASSIFICATION OF 3-GRADED CAUSAL SUBALGEBRAS OF REAL SIMPLE LIE ALGEBRAS. Transformation Groups. https://dx.doi.org/10.1007/s00031-020-09635-8
MLA:
Oeh, Daniel. "CLASSIFICATION OF 3-GRADED CAUSAL SUBALGEBRAS OF REAL SIMPLE LIE ALGEBRAS." Transformation Groups (2021).
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