Automorphism group of $\bar{B}$

Senthamarai Kannan Subramaniam; Aisha Negi

doi:10.5802/crmath.742

Research article - Algebra

Automorphism group of $\bar{B}$

Senthamarai Kannan Subramaniam ¹; Aisha Negi ¹

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

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

Abstract (Original language)
Résumé

Let $G$ be a simple algebraic group of adjoint type over the field of complex numbers, different from $\operatorname{PSL}(2,\mathbb{C})$. 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 $\operatorname{PSL}(2,\mathbb{C})$. 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 $B\times B$.

Received: 2024-07-01
Revised: 2025-03-06
Accepted: 2025-03-16
Published online: 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

Author's affiliations:

Senthamarai Kannan Subramaniam ¹ ; Aisha Negi ¹

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Automorphism group of $\bar{B}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {723--737},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     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

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