FAQ

Existence of complex structures on decomposable Lie algebras

Data publikacji: 2020

Universitatis Iagellonicae Acta Mathematica, 2020, Tom 57, s. 25 - 58

https://doi.org/10.4467/20843828AM.20.002.13312

Autorzy

Marcin Sroka
Faculty of Mathematics and Computer Science, Jagiellonian University ul. Łojasiewicza 6, 30-348 Kraków, Poland
Wszystkie publikacje autora →

Tytuły

Existence of complex structures on decomposable Lie algebras

Abstrakt

We provide the classification of the six-dimensional decomposable Lie algebras, with the dimension of the biggest indecomposable summand less than five, admitting complex structures. 

2010 Mathematics Subject Classification. 17B40, 53C15, 53C30.

Bibliografia

1. Andrada A., Barberis M.L., Dotti I., Classification of abelian complex structures on 6-dimensional Lie algebras, J. Lond. Math. Soc. (2), 83 (2011), 232–255.

2. Andrada A., Barberis M.L., Dotti I., Corrigendum: Classification of abelian complex structures on 6-dimensional Lie algebras, J. Lond. Math. Soc. (2), 87 (2013), 319–320.

3. Angella D., Otal A., Ugarte L., Villacampa R., Complex structures of splitting type, Rev. Mat. Iberoam., 33(4) (2017), 1309–1350.

4. Bianchi L., Sugli spazi a tre dimensioni che ammettono un gruppo continuo di movimenti, Mem. Soc. Ital. Scienze (3), 11 (1897), 267–352.

5. Blair D.E., Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Math. 203, Birkh¨auser, Boston, 2002.

6. Bock Ch., On low-dimensional solvmanifolds, Asian J. Math., 20(2) (2016), 199–262.

7. Ceballos M., Otal A., Ugarte L., Villacampa R., Invariant complex structures on 6-nilmanifolds: classification, Fr¨olicher spectral sequence and special Hermitian metrics, J. Geom. Anal., 26 (2016), 252–286.

8. Chevalley C., Eilenberg S., Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85–124.

9. Czarnecki A., Sroka M., Six-dimensional product Lie algebras admitting integrable complex structures, J. Pure Appl. Algebra, 222 (2018), 1111–1125.

10. Fino A., Otal A., Ugarte L., Six-dimensional solvmanifolds with holomorphically trivial canonical bundle, Int. Math. Res. Not. IMRN, 24 (2015), 13757–13799.

11. Freibert M., Schulte-Hengesbach F., Half-flat structures on decomposable Lie groups, Transform. Groups, 17(1) (2012), 123–141.

12. Magnin L., Left invariant complex structures on U(2) and SU(2)×SU(2) revisited, Rev. Roumaine Math. Pures Appl., 55 (2010), 269–296.

13. Morimoto A., Structures complexes sur les groupes de Lie semi-simples, C. R. Acad. Sci. Paris, 242 (1956), 1101–1103.

14. Morimoto A., On normal almost contact structures, J. Math. Soc. Japan, 15 (1963), 420–436.

15. Mubarakzjanov G.M., Classification of real structures of Lie algebras of order fifth (in Russian), Izv. Vyss. Ucebn. Zaved. Matematika, 35 (1963), 104–116.

16. Nomizu K., On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. (2), 59 (1954), 531–538.

17. Ovando G., Invariant complex structures on solvable real Lie groups, Manuscripta Math., 103 (2000), 19–30.

18. Patera J., Sharp R.T., Winternitz P., Zassenhaus H., Invariants of real low dimension Lie algebras, J. Mathematical Phys., 17 (1976), 986–994.

19. Salamon S.M., Complex structures on nilpotent Lie algebras, J. Pure Appl. Algebra, 157 (2001), 311–333.

20. Samelson H., A class of complex analytic manifolds, Portugal. Math., 12 (1953), 129–132.

21. Schulte-Hengesbach F., Half-flat structures on products of three-dimensional Lie groups, J. Geom. Phys., 60(11) (2010), 1726–1740.

22. Snow D.M., Invariant complex structures on reductive Lie groups, J. Reine Angew. Math., 371 (1986), 191–215.

23. Snow J.E., Invariant complex structures on four-dimensional solvable real lie groups, Manuscripta Math., 66 (1990), 397–412.

24. Wang H.C., Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), 1–32.

Informacje

Informacje: Universitatis Iagellonicae Acta Mathematica, 2020, Tom 57, s. 25 - 58

Typ artykułu: Oryginalny artykuł naukowy

Tytuły:

Angielski:

Existence of complex structures on decomposable Lie algebras

Polski:

Existence of complex structures on decomposable Lie algebras

Autorzy

Faculty of Mathematics and Computer Science, Jagiellonian University ul. Łojasiewicza 6, 30-348 Kraków, Poland

Publikacja: 2020

Status artykułu: Otwarte __T_UNLOCK

Licencja: CC BY-NC-ND  ikona licencji

Udział procentowy autorów:

Marcin Sroka (Autor) - 100%

Korekty artykułu:

-

Języki publikacji:

Angielski

Liczba wyświetleń: 1079

Liczba pobrań: 941

<p> Existence of complex structures on decomposable Lie algebras</p>