De Rham 2-Cohomology of Real Flag Manifolds
Let FΘ = G/PΘ be a flag manifold associated to a non-compact real simple Lie group G and the parabolic subgroup PΘ. This is a closed subgroup of G determined by a subset Θ of simple restricted roots of g = Lie(G). This paper computes the second de Rham cohomology group of FΘ. We prove that it is zer...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2019
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210244 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | De Rham 2-Cohomology of Real Flag Manifolds / V. del Barco, L.A.B. San Martin // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210244 |
|---|---|
| record_format |
dspace |
| spelling |
del Barco, V. San Martín, L.A.B. 2025-12-04T13:11:30Z 2019 De Rham 2-Cohomology of Real Flag Manifolds / V. del Barco, L.A.B. San Martin // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57T15; 14M15 arXiv: 1811.07854 https://nasplib.isofts.kiev.ua/handle/123456789/210244 https://doi.org/10.3842/SIGMA.2019.051 Let FΘ = G/PΘ be a flag manifold associated to a non-compact real simple Lie group G and the parabolic subgroup PΘ. This is a closed subgroup of G determined by a subset Θ of simple restricted roots of g = Lie(G). This paper computes the second de Rham cohomology group of FΘ. We prove that it is zero in general, with some rare exceptions. When it is non-zero, we give a basis of H²(FΘ, ℝ) through the Weil construction of closed 2-forms as characteristic forms of principal fiber bundles. The starting point is the computation of the second homology group of FΘ with coefficients in a ring R. V. del Barco supported by FAPESP grants 2015/23896-5 and 2017/13725-4. L.A.B. San Martin supported by CNPq grant 476024/2012-9 and FAPESP grant 2012/18780-0. The authors express their gratitude to Lonardo Rabelo for careful reading of a previous version of this manuscript and his useful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications De Rham 2-Cohomology of Real Flag Manifolds Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
De Rham 2-Cohomology of Real Flag Manifolds |
| spellingShingle |
De Rham 2-Cohomology of Real Flag Manifolds del Barco, V. San Martín, L.A.B. |
| title_short |
De Rham 2-Cohomology of Real Flag Manifolds |
| title_full |
De Rham 2-Cohomology of Real Flag Manifolds |
| title_fullStr |
De Rham 2-Cohomology of Real Flag Manifolds |
| title_full_unstemmed |
De Rham 2-Cohomology of Real Flag Manifolds |
| title_sort |
de rham 2-cohomology of real flag manifolds |
| author |
del Barco, V. San Martín, L.A.B. |
| author_facet |
del Barco, V. San Martín, L.A.B. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Let FΘ = G/PΘ be a flag manifold associated to a non-compact real simple Lie group G and the parabolic subgroup PΘ. This is a closed subgroup of G determined by a subset Θ of simple restricted roots of g = Lie(G). This paper computes the second de Rham cohomology group of FΘ. We prove that it is zero in general, with some rare exceptions. When it is non-zero, we give a basis of H²(FΘ, ℝ) through the Weil construction of closed 2-forms as characteristic forms of principal fiber bundles. The starting point is the computation of the second homology group of FΘ with coefficients in a ring R.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210244 |
| citation_txt |
De Rham 2-Cohomology of Real Flag Manifolds / V. del Barco, L.A.B. San Martin // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT delbarcov derham2cohomologyofrealflagmanifolds AT sanmartinlab derham2cohomologyofrealflagmanifolds |
| first_indexed |
2025-12-07T21:24:53Z |
| last_indexed |
2025-12-07T21:24:53Z |
| _version_ |
1850886264570511360 |