Complex structures on the complexification of a real Lie algebra
Let g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the scalar restriction. Conversely, let J̃ be an int...
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De Gruyter
2018-08-01
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| Series: | Complex Manifolds |
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| Online Access: | https://doi.org/10.1515/coma-2018-0010 |
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doaj-b0491356f00f474abb8aac5e789c09b42021-09-06T19:19:42ZengDe GruyterComplex Manifolds2300-74432018-08-015115015710.1515/coma-2018-0010coma-2018-0010Complex structures on the complexification of a real Lie algebraYamada Takumi0Department of Mathematics, Shimane University, Nishikawatsu-cho 1060,Matsue, JapanLet g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the scalar restriction. Conversely, let J̃ be an integrable complex structure on h = ℝ(gℂ). Then, we have a direct sum decomposition g = a + b such that a and b are Lie subalgebras. We also investigate relations between the decomposition g = a + b and dim Hs.t∂̄J̃ (hℂ).https://doi.org/10.1515/coma-2018-0010nilmanifolddolbeault cohomology groupcomplex structure53c3057t1522e25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yamada Takumi |
| spellingShingle |
Yamada Takumi Complex structures on the complexification of a real Lie algebra Complex Manifolds nilmanifold dolbeault cohomology group complex structure 53c30 57t15 22e25 |
| author_facet |
Yamada Takumi |
| author_sort |
Yamada Takumi |
| title |
Complex structures on the complexification of a real Lie algebra |
| title_short |
Complex structures on the complexification of a real Lie algebra |
| title_full |
Complex structures on the complexification of a real Lie algebra |
| title_fullStr |
Complex structures on the complexification of a real Lie algebra |
| title_full_unstemmed |
Complex structures on the complexification of a real Lie algebra |
| title_sort |
complex structures on the complexification of a real lie algebra |
| publisher |
De Gruyter |
| series |
Complex Manifolds |
| issn |
2300-7443 |
| publishDate |
2018-08-01 |
| description |
Let g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the scalar restriction. Conversely, let J̃ be an integrable complex structure on h = ℝ(gℂ). Then, we have a direct sum decomposition g = a + b such that a and b are Lie subalgebras. We also investigate relations between the decomposition g = a + b and dim Hs.t∂̄J̃ (hℂ). |
| topic |
nilmanifold dolbeault cohomology group complex structure 53c30 57t15 22e25 |
| url |
https://doi.org/10.1515/coma-2018-0010 |
| work_keys_str_mv |
AT yamadatakumi complexstructuresonthecomplexificationofarealliealgebra |
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1717777987422650368 |