The reductive pair \((B_4, B_3)\) and affine connections on \(S^{15}\) (Q1569809)
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scientific article; zbMATH DE number 1471030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The reductive pair \((B_4, B_3)\) and affine connections on \(S^{15}\) |
scientific article; zbMATH DE number 1471030 |
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The reductive pair \((B_4, B_3)\) and affine connections on \(S^{15}\) (English)
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9 July 2000
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The authors continue their investigations of reductive pairs of Lie algebras \((L,H)\). In particular they determine the attached connection algebras and related tensors for \((B_4, B_3)\). When restricted to the real field, it is shown that there is a three parameter family of Spin(9)-invariant affine connections on \(S^{15}\). They find five different possibilities for the holonomy algebra of a connection algebra attached to \((B_4, B_3)\).
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reductive pairs of Lie algebras
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affine connections
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holonomy algebra
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connection algebra
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