Geodesic
The Push-the-Button Algorithm for Contragredient Lie Superalgebras
Séminaire lotharingien de combinatoire, Tome 75 (2016-2019)

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We apply the idea of the "push-the-button" algorithm, introduced by Chuah and Hu in [J. Algebra 279 (2004), 22-37], to the Vogan superdiagram associated to a contragredient Lie superalgebra. We obtain the Borel-de Siebenthal Theorem in the supersetting, leading to the classification of the real forms of contragredient Lie superalgebras (previously discussed in [V.~G.~Kac, Adv. Math. 26 (1977), 8-96; V.~Serganova, Funkt. Anal. Prilozhen. 17 (1983), 46-54; M.~Parker, J. Math. Phys. 21 (1980), 689-798]). 

@article{SLC_2016-2019_75_a8,
     author = {Rita Fioresi and Riccardo Palmieri},
     title = {The {Push-the-Button} {Algorithm} for {Contragredient} {Lie} {Superalgebras}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {75},
     year = {2016-2019},
     url = {http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a8/}
}
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Rita Fioresi; Riccardo Palmieri. The Push-the-Button Algorithm for Contragredient Lie Superalgebras. Séminaire lotharingien de combinatoire, Tome 75 (2016-2019). http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a8/