Adjoint algebraic groups as automorphism groups of a projector on a central simple algebra

We show that any adjoint absolutely simple linear algebraic group over a field of characteristic zero is the automorphism group of some projector on a central simple algebra. Projective homogeneous varieties can be described in these terms; in particular, we reproduce quadratic equations by Lichtens...

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Bibliographic Details
Published in:Journal of algebra 2020-10, Vol.560, p.574-578
Main Authors: Petrov, Viktor A., Semenov, Andrei V.
Format: Article
Language:English
Subjects:
Algebraic groups
Casimir operator
Central simple algebras
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Summary:We show that any adjoint absolutely simple linear algebraic group over a field of characteristic zero is the automorphism group of some projector on a central simple algebra. Projective homogeneous varieties can be described in these terms; in particular, we reproduce quadratic equations by Lichtenstein defining them.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.06.006