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Complex product structures on Lie algebras
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Adrián Andrada
Veröffentlicht/Copyright:
27. Juli 2005
Abstract
A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. Any Lie algebra ɡ with such a structure is even-dimensional and its complexification has a hypercomplex structure. In addition, ɡ splits into the direct sum of two Lie subalgebras of the same dimension, and each of these is shown to have a left-symmetric algebra (LSA) structure. Interpretations of these results are obtained that are relevant to the theory of both hypercomplex and hypersymplectic manifolds and their associated connections.
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Published Online: 2005-07-27
Published in Print: 2005-03-11
© de Gruyter
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Artikel in diesem Heft
- Defect relation for rational functions as targets
- On the structure of distributive and Bezout rings with waists
- The dimension of spheres with smooth one fixed point actions
- Space curves and trisecant lines
- Convergence of Dirichlet forms with changing speed measures on ℝd
- Complex product structures on Lie algebras
- Homogeneous spaces in coincidence theory II
- Holomorphic convexity of complex spaces with 1-convex hypersections
- The Nielsen numbers of Anosov diffeomorphisms on flat Riemannian manifolds
Artikel in diesem Heft
- Defect relation for rational functions as targets
- On the structure of distributive and Bezout rings with waists
- The dimension of spheres with smooth one fixed point actions
- Space curves and trisecant lines
- Convergence of Dirichlet forms with changing speed measures on ℝd
- Complex product structures on Lie algebras
- Homogeneous spaces in coincidence theory II
- Holomorphic convexity of complex spaces with 1-convex hypersections
- The Nielsen numbers of Anosov diffeomorphisms on flat Riemannian manifolds
