Elements in Pointed Invariant Cones in Lie Algebras and Corresponding Affine Pairs

Neeb KH, Oeh D (2021)


Publication Type: Journal article

Publication year: 2021

Journal

DOI: 10.1007/s41980-021-00671-y

Abstract

In this note, we study in a finite dimensional Lie algebra g the set of all those elements x for which the closed convex hull of the adjoint orbit contains no affine lines; this contains in particular elements whose adjoint orbits generates a pointed convex cone C-x. Assuming that g is admissible, i.e., contains a generating invariant convex subset not containing affine lines, we obtain a natural characterization of such elements, also for non-reductive Lie algebras. Motivated by the concept of standard (Borchers) pairs in QFT, we also study pairs (x, h) of Lie algebra elements satisfying [h, x] = x for which Cx pointed. Given x, we show that such elements h can be constructed in such a way that ad h defines a 5-grading, and characterize the cases where we even get a 3-grading.

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How to cite

APA:

Neeb, K.-H., & Oeh, D. (2021). Elements in Pointed Invariant Cones in Lie Algebras and Corresponding Affine Pairs. Bulletin of the Iranian Mathematical Society. https://dx.doi.org/10.1007/s41980-021-00671-y

MLA:

Neeb, Karl-Hermann, and Daniel Oeh. "Elements in Pointed Invariant Cones in Lie Algebras and Corresponding Affine Pairs." Bulletin of the Iranian Mathematical Society (2021).

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