Invariant generalized complex structures on flag manifolds

Autor(es)

Varea, Carlos A. B. ^[1] ; San Martin, Luiz A. B. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRY AND PHYSICS; v. 150, APR 2020.
• Citações Web of Science: 0

Resumo

Let G be a complex semi-simple Lie group and form its maximal flag manifold F = G/P = U/T where P is a minimal parabolic subgroup, U a compact real form and T = U boolean AND P a maximal torus of U. The aim of this paper is to study invariant generalized complex structures on F. We describe the invariant generalized almost complex structures on F and classify which one is integrable. The problem reduces to the study of invariant 4-dimensional generalized almost complex structures restricted to each root space, and for integrability we analyze the Nijenhuis operator for a triple of roots such that its sum is zero. We also conducted a study about twisted generalized complex structures. We define a new bracket twisted' by a closed 3-form Omega and also define the Nijenhuis operator twisted by Omega. We classify the Omega-integrable generalized complex structure. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 16/07029-2 - Estruturas complexas generalizadas invariantes em espaços homogêneos
• Beneficiário: Carlos Augusto Bassani Varea
• Modalidade de apoio: Bolsas no Brasil - Doutorado