Journal of Lie Theory

no. 2
Heisenberg Algebras from Division Algebras and Parabolic Subalgebras of Simple Lie Algebras
Aroldo Kaplan1, 2; Mauro Subils3
1Dept. of Mathematics, University of Massachusetts, Amherst, MA01002, U.S.A.
2CONICET-CIEM, Universidad Nacional de Cordoba, Medina Allende, Cordoba 5000, Argentina
3CONICET-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario 2000, Argentina
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 561-575
Every real simple Lie algebra which is not compact or isomorphic to so(1,n) contains a unique standard parabolic subalgebra whose nilradical is a Heisenberg-like algebra associated to a division algebra. Some geometric consequences are discussed.
DOI: 10.5802/jolt.1013
Classification: 22E25, 58A30, 17C60
Keywords: Heisenberg, parabolic subalgebras, distributions

Aroldo Kaplan  1 , 2 ; Mauro Subils  3

1 Dept. of Mathematics, University of Massachusetts, Amherst, MA01002, U.S.A.
2 CONICET-CIEM, Universidad Nacional de Cordoba, Medina Allende, Cordoba 5000, Argentina
3 CONICET-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario 2000, Argentina 
Aroldo Kaplan; Mauro Subils. Heisenberg Algebras from Division Algebras and Parabolic Subalgebras of Simple Lie Algebras. Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 561-575. doi: 10.5802/jolt.1013
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     author = {Aroldo Kaplan and Mauro Subils},
     title = {Heisenberg {Algebras} from {Division} {Algebras} and {Parabolic} {Subalgebras} of {Simple} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {561--575},
     year = {2018},
     volume = {28},
     number = {2},
     doi = {10.5802/jolt.1013},
     zbl = {1395.22002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1013/}
}
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