Loterre: Matemáticas: generalized flag variety

geometry > algebraic geometry > generalized flag variety

... > manifold > differentiable manifold > Lie group > homogeneous space > generalized flag variety

... > differential geometry > differentiable manifold > Lie group > homogeneous space > generalized flag variety

... > differential topology > differentiable manifold > Lie group > homogeneous space > generalized flag variety

... > group theory > topological group > Lie group > homogeneous space > generalized flag variety

algebra > abstract algebra > algebraic structure > homogeneous space > generalized flag variety

generalized flag variety

In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieties are naturally projective varieties. Flag varieties can be defined in various degrees of generality. A prototype is the variety of complete flags in a vector space V over a field F, which is a flag variety for the special linear group over F. Other flag varieties arise by considering partial flags, or by restriction from the special linear group to subgroups such as the symplectic group. For partial flags, one needs to specify the sequence of dimensions of the flags under consideration. For subgroups of the linear group, additional conditions must be imposed on the flags.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Generalized_flag_variety)

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