• Thumbnail for Reductive group
    field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some...
    55 KB (7,845 words) - 18:28, 24 April 2024
  • reductive groups, but over non-perfect fields Jacques Tits found some examples of pseudo-reductive groups that are not reductive. A pseudo-reductive k-group...
    8 KB (1,102 words) - 15:39, 16 February 2024
  • Thumbnail for Linear algebraic group
    require reductive groups to be connected.) A semisimple group is reductive. A group G over an arbitrary field k is called semisimple or reductive if G k...
    41 KB (6,000 words) - 12:59, 4 October 2024
  • Thumbnail for Algebraic group
    a semidirect product of a unipotent group (its unipotent radical) with a reductive group. In turn reductive groups are decomposed as (again essentially)...
    16 KB (2,244 words) - 11:33, 24 September 2024
  • Reductive amination (also known as reductive alkylation) is a form of amination that involves the conversion of a carbonyl group to an amine via an intermediate...
    21 KB (2,134 words) - 19:54, 6 October 2024
  • Thumbnail for Group of Lie type
    in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear...
    22 KB (2,985 words) - 10:42, 28 March 2023
  • Langlands program (category Representation theory of Lie groups)
    for one semisimple (or reductive) Lie group, should be done for all. Therefore, once the role of some low-dimensional Lie groups such as GL(2) in the theory...
    26 KB (2,934 words) - 10:29, 25 October 2024
  • Thumbnail for Group homomorphism
    In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it...
    10 KB (1,531 words) - 12:55, 1 October 2024
  • the unipotent radical, it serves to define reductive groups. Reductive group Unipotent group "Radical of a group", Encyclopaedia of Mathematics v t e...
    1 KB (148 words) - 12:23, 13 August 2023
  • Thumbnail for Poincaré group
    The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It...
    15 KB (2,173 words) - 17:44, 15 August 2024