Automorphism group of $\bar{B}$

Senthamarai Kannan Subramaniam; Aisha Negi

doi:10.5802/crmath.742

Article de recherche - Algèbre

Automorphism group of

\bar{B}

[Groupe d’automorphismes de

\bar{B}

]

Senthamarai Kannan Subramaniam ¹ ; Aisha Negi ¹

¹ Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 723-737.

Abstract (VO)
Résumé

Let $G$ be a simple algebraic group of adjoint type over the field of complex numbers, different from $PSL (2, C)$ . Let $\bar{G}$ be the wonderful compactification of $G$ constructed by C. De Concini and C. Procesi. Let $\bar{B}$ be the scheme theoretic closure of a Borel subgroup $B$ of $G$ in $\bar{G}$ . Then we prove that the connected component, containing the identity automorphism of the group of all algebraic automorphisms of $\bar{B}$ is $B \times B$ .

Soit $G$ un groupe algébrique simple de type adjoint sur le corps des nombres complexes, différent de $PSL (2, C)$ . Soit $\bar{G}$ la compactification magnifique de $G$ construite par C. De Concini et C. Procesi. Soit $\bar{B}$ l’adhérence de Zariski d’un sous-groupe borélien $B$ de $G$ dans $\bar{G}$ . Nous prouvons que la composante connexe, contenant l’automorphisme identitaire du groupe de tous les automorphismes algébriques de $\bar{B}$ est $B \times B$ .

Reçu le : 2024-07-01
Révisé le : 2025-03-06
Accepté le : 2025-03-16
Publié le : 2025-06-24

DOI : 10.5802/crmath.742

Classification : 14L10, 14L30
Keywords: Automorphism groups, wonderful compactification, unipotent group
Mots-clés : Groupes d’automorphismes, compactification magnifique, groupe unipotent

Affiliations des auteurs :

Senthamarai Kannan Subramaniam ¹ ; Aisha Negi ¹

¹ Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Senthamarai Kannan Subramaniam and Aisha Negi},
     title = {Automorphism group of $\bar{B}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {723--737},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.742},
     language = {en},
}

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Senthamarai Kannan Subramaniam; Aisha Negi. Automorphism group of $\bar{B}$. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 723-737. doi : 10.5802/crmath.742. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.742/

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