Geodesic
Admissible Systems and Graded Hermitian Superspaces
Meng-Kiat Chuah1 ; Rita Fioresi2, 3 ; Fabio Gavarini4, 5
1Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
2(1) FaBiT, University of Bologna, Italy
3(2) INFN, Sezione Bologna, Italy
4(1) Dip. di Matematica, University of Rome ``Tor Vergata'', Roma, Italy
5(2) Istituto Nazionale di Alta Matematica / GNSAGA, Roma, Italy
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 617-628

Voir la notice de l'article provenant de la source Heldermann Verlag

We introduce the notion of admissible systems for involutions on complex contragredient Lie superalgebras, and classify the involutions with admissible systems by circlings on extended Dynkin diagrams. We prove the graded Iwasawa decomposition of the symmetric pair (g, k) consisisting of the contragredient Lie superalgebra g and the fixed points of an involution. We also show the representability in the category of complex superspaces of the corresponding real symmetric superspace.
Classification : 17B20, 17B22, 17B40
Mots-clés : Contragredient Lie superalgebras, involutions, admissible systems, real forms, Dynkin diagrams

Meng-Kiat Chuah  1   ; Rita Fioresi  2 , 3   ; Fabio Gavarini  4 , 5

1 Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
2 (1) FaBiT, University of Bologna, Italy
3 (2) INFN, Sezione Bologna, Italy
4 (1) Dip. di Matematica, University of Rome ``Tor Vergata'', Roma, Italy
5 (2) Istituto Nazionale di Alta Matematica / GNSAGA, Roma, Italy 
Meng-Kiat Chuah; Rita Fioresi; Fabio Gavarini. Admissible Systems and Graded Hermitian Superspaces. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 617-628. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a8/
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     title = {Admissible {Systems} and {Graded} {Hermitian} {Superspaces}},
     journal = {Journal of Lie Theory},
     pages = {617--628},
     year = {2025},
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     number = {3},
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