Existence of Hermitian n-symmetric spaces of non-commutative naturally reductive spaces (Q1088165)
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scientific article; zbMATH DE number 3990290
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of Hermitian n-symmetric spaces of non-commutative naturally reductive spaces |
scientific article; zbMATH DE number 3990290 |
Statements
Existence of Hermitian n-symmetric spaces of non-commutative naturally reductive spaces (English)
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1987
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It is shown that for each \(n>2\), the space SU(n)/T, T a maximal torus, has the following properties: (i) The space is Hermitian n-symmetric but not m-symmetric for \(m<n\). (ii) The identity component of the full group of isometries of any SU(n)-invariant metric is precisely \(SU(n)/Z_ n\). (iii) If SU(n)/T is endowed with the metric induced by the Killing form of SU(n), then it is naturally reductive but noncommutative. Similar results are stated for the other classical Lie groups.
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maximal torus
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classical Lie groups
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Hermitian n-symmetric space
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commutative space
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naturally reductive homogeneous space
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0.95402104
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0.8913559
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0.8766252
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0.87486076
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0.86899257
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0.8678756
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