Lattice isomorphisms of Lie algebras and algebraic groups (Q1089425)
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scientific article; zbMATH DE number 4004429
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lattice isomorphisms of Lie algebras and algebraic groups |
scientific article; zbMATH DE number 4004429 |
Statements
Lattice isomorphisms of Lie algebras and algebraic groups (English)
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1987
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Let L be a simple Lie algebra of relative rank \(\geq 2\). Then for every lattice isomorphism \(\phi\) between L and a Lie algebra L' there exists a unique semilinear isomorphism between L and L' induced by \(\phi\) on the set of all parabolic subalgebras of L. The corresponding result for lattice isomorphisms of algebraic groups is obtained, too.
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subalgebra lattices
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subgroup lattices
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simple Lie algebra
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lattice isomorphisms
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algebraic groups
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