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On the geometry of the adjoint representation of a Chevalley group - MaRDI portal

On the geometry of the adjoint representation of a Chevalley group (Q1263673)

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scientific article; zbMATH DE number 4127499
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English
On the geometry of the adjoint representation of a Chevalley group
scientific article; zbMATH DE number 4127499

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    On the geometry of the adjoint representation of a Chevalley group (English)
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    1989
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    Let L be the Lie algebra of a linear algebraic group G over a field of arbitrary characteristic. The subalgebras of L corresponding to long root subgroups are called long root subalgebras of L. Subalgebras of L generated by long root subalgebras are called long subalgebras. The main theorem: Let L correspond to a simple group G of type different from \(C_ n\) and \(A_ 1\). Then L has a presentation with generators the elements of its long root subalgebras, subject to those relations that hold inside long \(A_ 2\)-subalgebras.
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    Lie algebra of a linear algebraic group
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    long root subgroups
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    long root subalgebras
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    presentation
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