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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| Format: | Article |
| Language: | English |
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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 |
| _version_ | 1818723116846678016 |
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| author | Yamada Takumi |
| author_facet | Yamada Takumi |
| author_sort | Yamada Takumi |
| collection | DOAJ |
| 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). |
| first_indexed | 2024-12-17T21:05:25Z |
| format | Article |
| id | doaj.art-b0491356f00f474abb8aac5e789c09b4 |
| institution | Directory Open Access Journal |
| issn | 2300-7443 |
| language | English |
| last_indexed | 2024-12-17T21:05:25Z |
| publishDate | 2018-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Complex Manifolds |
| spelling | doaj.art-b0491356f00f474abb8aac5e789c09b42022-12-21T21:32:36ZengDe 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 |
| spellingShingle | Yamada Takumi Complex structures on the complexification of a real Lie algebra Complex Manifolds nilmanifold dolbeault cohomology group complex structure 53c30 57t15 22e25 |
| title | 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_short | Complex structures on the complexification of a real Lie algebra |
| title_sort | complex structures on the complexification of a real lie algebra |
| 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 |