algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the...

{\displaystyle \mathbb {C} } , and fix a maximal torus T along with a Borel subgroup B which contains T. Let λ be an integral weight of T; λ defines in a...

two of the Borel subgroups. The example given above, the subgroup B {\displaystyle B} in G L 2 {\displaystyle GL_{2}} , is a Borel subgroup. In G L 3 {\displaystyle...

algebra. These are, respectively, the standard Borel subgroup B of the Lie group GLn and the standard Borel subalgebra b {\displaystyle {\mathfrak {b}}}...

called the Borel subgroup of G L ( n ) {\displaystyle GL(n)} . It is a consequence of the Lie-Kolchin theorem that any connected solvable subgroup of G L...

 452) Borel–Weil–Bott theorem Borel cohomology Borel conjecture Borel construction Borel subgroup Borel subalgebra Borel fixed-point theorem Borel's theorem...

Parabolic subgroup may refer to: a parabolic subgroup of a reflection group a subgroup of an algebraic group that contains a Borel subgroup This disambiguation...

it contains a Borel subgroup over k. A split reductive group is quasi-split. If G is quasi-split over k, then any two Borel subgroups of G are conjugate...

variety Borel subgroup Tame group Morley rank Cherlin–Zilber conjecture Adelic algebraic group Pseudo-reductive group Borel 1991, p.54. Borel 1991, p...

the Lie algebra of a complex Lie group, then a Borel subalgebra is the Lie algebra of a Borel subgroup. Let g = g l ( V ) {\displaystyle {\mathfrak {g}}={\mathfrak...