Journal of Lie Theory

no. 2
Invariant Orders on Hermitian Lie Groups
Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 437-463
We study three natural bi-invariant partial orders on a certain covering group of the automorphism group of a bounded symmetric domain of tube type; these orderings are defined using the geometry of the Shilov boundary, Lie semigroup theory and quasimorphisms respectively. Our main result shows that these orders are related by two inclusion relations. In the case of SL2(R), where R stands for the real numbers, we can show that they coincide. We also prove a related coincidence of orders for the universal covering of the group of homeomorphisms of the circle.
DOI: 10.5802/jolt.674
Classification: 06A06, 06F15, 11E57, 22E46, 51L99
Keywords: Hermitian Lie groups, invariant orders, quasimorphisms, Lie semigroups, bounded cohomology 
@article{JOLT_2012_22_2_a3,
     author = {G. Ben Simon and T. Hartnick},
     title = {Invariant {Orders} on {Hermitian} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {437--463},
     year = {2012},
     volume = {22},
     number = {2},
     doi = {10.5802/jolt.674},
     zbl = {1254.22008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.674/}
}
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G. Ben Simon; T. Hartnick. Invariant Orders on Hermitian Lie Groups. Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 437-463. doi: 10.5802/jolt.674

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