Invariant Complex Structures on Tangent and Cotangent Lie Groups of Dimension Six

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dc.contributor.authorCampoamor Stursberg, Otto-Rudwig
dc.contributor.authorOvando, Gabriela P.
dc.date.accessioned2023-06-20T03:31:53Z
dc.date.available2023-06-20T03:31:53Z
dc.date.issued2012
dc.description.abstractThis paper deals with left invariant complex structures on simply connected Lie groups, the Lie algebra of which is of the type Th D hË V, where is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on Th for h a three dimensional real Lie algebra. First it was proposed the study of complex structures J satisfying the constraint Jh D V. Whenever is the adjoint representation this kind of complex structures are associated to non-singular derivations of h. This fact allows different kinds of applications.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipCONICET, ANPCyT, SECyT-UNC, SCyT-UNR
dc.description.sponsorshipMICINN
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20735
dc.identifier.citationA. Andrada, M.L. Barberis and I. Dotti: Classification of abelian complex structures on 6-dimensional Lie algebras, J. Lond. Math. Soc. (2) 83 (2011), 232–255. L.C. de Andrés, M.L. Barberis, I. Dotti and M. Fernández: Hermitian structures on cotangent bundles of four dimensional solvable Lie groups, Osaka J. Math. 44 (2007), 765–793. A. Andrada, M.L. Barberis and G. Ovando: Lie bialgebras of complex type and associated Poisson Lie groups, J. Geom. Phys. 58 (2008), 1310–1328. M.L. Barberis and I.G. Dotti: Complex structures on affine motion groups, Q.J. Math. 55 (2004), 375–389. M.L. Barberis, I.G. Dotti Miatello and R.J. Miatello: On certain locally homogeneous Clifford manifolds, Ann. Global Anal. Geom. 13 (1995), 289–301. M.N. Boyom: Variétés symplectiques affines,Manuscripta Math. 64 (1989), 1–33. R. Cleyton, J. Lauret and Y.S. Poon: Weak mirror symmetry of Lie algebras, J. Symplectic Geom. 8 (2010), 37–55. R. Cleyton, G. Ovando and Y.S. Poon: Weak mirror symmetry of complex symplectic Lie algebras, J. Geom. Phys. 61 (2011), 1553–1563. L.A. Cordero, M. Fernández, A. Gray and L. Ugarte: Nilpotent complex structures on compact nilmanifolds, Rend. Circ. Mat. Palermo (2) Suppl. 49 (1997), 83–100. L.A. Cordero, M. Fernández, A. Gray and L. Ugarte: Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology, Trans. Amer. Math. Soc. 352 (2000), 5405–5433. L.A. Cordero, M. Fernández and L. Ugarte: Pseudo-Kähler metrics on six-dimensional nilpotent Lie algebras, J. Geom. Phys. 50 (2004), 115–137. G.R. Cavalcanti and M. Gualtieri: Generalized complex structures on nilmanifolds, J. Symplectic Geom. 2 (2004), 393–410. R. Campoamor Stursberg and G. Ovando: Complex structures on tangent and cotangent Lie algebras, arXiv:math.DG/0805.2520. A. Fino, M. Parton and S. Salamon: Families of strong KT structures in six dimensions, Comment. Math. Helv. 79 (2004), 317–340. V. Gorbatsevich, A. Onishchik and E.Vinberg: Lie Groups and Lie Algebras, III, Encyclopaedia of Mathematical Sciences 41, Springer, Berlin, 1994. M. Gualtieri: Generalized complex geometry, Ph.D. Thesis, Univ. of Oxford, 2003, arxiv:math.DG/0401221. L. García Vergnolle and E. Remm: Complex structures on quasi-filiform Lie algebras, J. Lie Theory 19 (2009), 251–265. N. Hitchin: Generalized Calabi-Yau manifolds, Q.J. Math. 54 (2003), 281–308. N. Jacobson: A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc. 6 (1955), 281–283. J. Milnor: Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), 293–329. L. Magnin: Complex structures on indecomposable 6-dimensional nilpotent real Lie algebras, Internat. J. Algebra Comput. 17 (2007), 77–113. G. Ovando: Invariant complex structures on solvable real Lie groups, Manuscripta Math. 103 (2000), 19–30. G. Ovando: Invariant pseudo-Kähler metrics in dimension four, J. Lie Theory 16 (2006), 371–391. P. Petravchuk: Lie algebras decomposable as a sum of an abelian and a nilpotent subalgebra, Ukr. Math. J. 40 (1988), 385–388. T. Sasaki: Classification of left invariant complex structures onGL(2, R) and U(2), Kumamoto J. Sci. (Math.) 14 (1980), 115–123. T. Sasaki: Classification of invariant complex structures on SL(3, R),Kumamoto J. Sci. (Math.) 15 (1982), 59–72. H. Samelson: A class of complex-analytic manifolds, Portugaliae Math. 12 (1953), 129–132. D.M. Snow: Invariant complex structures on reductive Lie groups, J. Reine Angew. Math. 371 (1986), 191–215. J.E. Snow: Invariant complex structures on four-dimensional solvable real Lie groups, Manuscripta Math. 66 (1990), 397–412. T. Sasaki: Classification of left invariant complex structures onGL(2, R) andU(2),Kumamoto J. Sci. (Math.) 14 (1981), 115–123. S.M. Salamon: Complex structures on nilpotent Lie algebras, J. Pure Appl. Algebra 157 (2001), 311–333. M. Tekkoyun: On para-Euler-Lagrange and para-Hamiltonian equations, Phys. Lett. A 340 (2005), 7–11. L. Ugarte: Hermitian structures on six-dimensional nilmanifolds, Transform. Groups 12 (2007), 175–202. H.-C.Wang: Closed manifolds with homogeneous complex structure, Amer. J. Math. 76 (1954), 1–32.
dc.identifier.issn0030-6126
dc.identifier.officialurlhttp://ir.library.osaka-u.ac.jp/dspace/bitstream/11094/8992/1/ojm49_02_489.pdf
dc.identifier.relatedurlhttp://ir.library.osaka-u.ac.jp/dspace/
dc.identifier.relatedurlhttp://hdl.handle.net/11094/8992
dc.identifier.urihttps://hdl.handle.net/20.500.14352/43741
dc.issue.number2
dc.journal.titleOsaka Journal of Mathematics
dc.language.isoeng
dc.page.final513
dc.page.initial489
dc.publisherOsaka University
dc.relation.projectIDMTM2010-18556
dc.rights.accessRightsrestricted access
dc.subject.cdu530.145
dc.subject.keywordComplex structures
dc.subject.keywordLie algebras
dc.subject.keywordsymplectic structures
dc.subject.ucmTeoría de los quanta
dc.subject.unesco2210.23 Teoría Cuántica
dc.titleInvariant Complex Structures on Tangent and Cotangent Lie Groups of Dimension Six
dc.typejournal article
dc.volume.number49
dspace.entity.typePublication
relation.isAuthorOfPublication72801982-9f3c-4db0-b765-6e7b4aa2221b
relation.isAuthorOfPublication.latestForDiscovery72801982-9f3c-4db0-b765-6e7b4aa2221b
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