SHA-RIGIDITY OF ADJOINT CHEVALLEY GROUPS OF TYPES A1, A2, B2, G2 OVER COMMUTATIVE RINGS

Elena Bunina; Vazgen Kirakosyan; Rachel Treskunov

doi:10.46298/jgcc.2026.18.2.17981

SHA-RIGIDITY OF ADJOINT CHEVALLEY GROUPS OF TYPES A₁, A₂, B₂, G₂ OVER COMMUTATIVE RINGS

Elena Bunina
, Vazgen Kirakosyan
, Rachel Treskunov

Department of Mathematics

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that every class-preserving endomorphism of the adjoint Chevalley group and of its elementary subgroup over a commutative ring is inner for the types A1, A2, and B2 when 2 is invertible, and for type G2 when 2 and 3 are invertible. Consequently, all these groups are Sha-rigid.

Original language	English
Journal	Groups, Complexity, Cryptology
Volume	18
Issue number	2
DOIs	https://doi.org/10.46298/jgcc.2026.18.2.17981
State	Published - 2026

Bibliographical note

Publisher Copyright:
© E. Bunina, V. Kirakosyan, and R. Treskunov.

Keywords

Chevalley groups
Sha-rigidity
class-preserving endomorphisms
commutative rings
locally inner endomorphisms

Access to Document

10.46298/jgcc.2026.18.2.17981

Cite this

@article{b6a2503b1d394c16894f8381bb1c8bf4,

title = "SHA-RIGIDITY OF ADJOINT CHEVALLEY GROUPS OF TYPES A1, A2, B2, G2 OVER COMMUTATIVE RINGS",

abstract = "We prove that every class-preserving endomorphism of the adjoint Chevalley group and of its elementary subgroup over a commutative ring is inner for the types A1, A2, and B2 when 2 is invertible, and for type G2 when 2 and 3 are invertible. Consequently, all these groups are Sha-rigid.",

keywords = "Chevalley groups, Sha-rigidity, class-preserving endomorphisms, commutative rings, locally inner endomorphisms",

author = "Elena Bunina and Vazgen Kirakosyan and Rachel Treskunov",

note = "Publisher Copyright: {\textcopyright} E. Bunina, V. Kirakosyan, and R. Treskunov.",

year = "2026",

doi = "10.46298/jgcc.2026.18.2.17981",

language = "אנגלית",

volume = "18",

journal = "Groups, Complexity, Cryptology",

issn = "1867-1144",

publisher = "Episciences",

number = "2",

}

TY - JOUR

T1 - SHA-RIGIDITY OF ADJOINT CHEVALLEY GROUPS OF TYPES A1, A2, B2, G2 OVER COMMUTATIVE RINGS

AU - Bunina, Elena

AU - Kirakosyan, Vazgen

AU - Treskunov, Rachel

N1 - Publisher Copyright: © E. Bunina, V. Kirakosyan, and R. Treskunov.

PY - 2026

Y1 - 2026

N2 - We prove that every class-preserving endomorphism of the adjoint Chevalley group and of its elementary subgroup over a commutative ring is inner for the types A1, A2, and B2 when 2 is invertible, and for type G2 when 2 and 3 are invertible. Consequently, all these groups are Sha-rigid.

AB - We prove that every class-preserving endomorphism of the adjoint Chevalley group and of its elementary subgroup over a commutative ring is inner for the types A1, A2, and B2 when 2 is invertible, and for type G2 when 2 and 3 are invertible. Consequently, all these groups are Sha-rigid.

KW - Chevalley groups

KW - Sha-rigidity

KW - class-preserving endomorphisms

KW - commutative rings

KW - locally inner endomorphisms

UR - https://www.scopus.com/pages/publications/105037200791

U2 - 10.46298/jgcc.2026.18.2.17981

DO - 10.46298/jgcc.2026.18.2.17981

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105037200791

SN - 1867-1144

VL - 18

JO - Groups, Complexity, Cryptology

JF - Groups, Complexity, Cryptology

IS - 2

ER -