Reductive group
A reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is ...
In the 1950s Chevalley became interested in algebraic groups as a link between complex. Lie algebras and finite groups. In a fundamental paper, Chevalley (1955) ...
What is the defining property of reductive groups and why are they ...
3 Answers 3 ... A linear algebraic group is unipotent if it consists entirely of unipotent linear transformations, i.e. I+N with N nilpotent. A ...
What is reductive group intuitively? - Mathematics Stack Exchange
We say that an affine algebraic group G is linearly reductive if all finite dimensional G-modules are semi-simple.
is the category of representations (i.e. homomorphisms into some general linear group). Thus, in words, the above says that reductive groups are ...
Definition 1.1. A Lie group G G is called reductive if its Lie algebra 𝔤 \mathfrak{g} is reductive, i.e., a direct sum of an abelian and a ...
Reductive group - Encyclopedia of Mathematics
A reductive group is a linear algebraic group G (over an algebraically closed field K) that satisfies one of the following equivalent conditions.
basics on reductive groups - Yale Math
All maximal tori are conjugate. From now and until the end of the section on algebraic groups we assume that. G is a connected reductive group. Let T ⊂ G ...
Reductive Groups over Fields - Stanford Mathematics
Linear algebraic groups. Let's review some notions from the previous course. Definition 1.1.1. For a field k, a linear algebraic group over k is ...
complex reductive algebraic groups - UBC Math
Strikingly, affine algebraic groups can all be realized as an algebraic subgroup of some GLn,K [Hum75, Theorem 8.6]. For instance, the special linear group SLn, ...
forms and covers of reductive groups, and the
Theorem 1.10 (Classification over the separable closure). Assume k separably closed. Given a connected reductive group G and a maximal torus T, the quadruple. Ψ ...
REDUCTIVE GROUP SCHEMES Brian Conrad
Abstract. — We develop the relative theory of reductive group schemes, using dynamic techniques and algebraic spaces to streamline the original ...
Reductive Lie algebra - Wikipedia
... reductive Lie group should be done for all. The intersection of reductive Lie algebras and solvable Lie algebras is exactly abelian ...
Notes on representations of real reduction groups math 224, spring ...
Compact Lie groups vs complex reductive algebraic groups. 4.1.1. Recall that an algebraic group is said to be reductive if its unipotent radical is trivial.
Reductive, linearly reductive, and geometrically reductive affine ...
In this class we studied reductive affine algebraic group. But in a class on Geometric Invariant Theory (GIT), it is more common to work ...
In many posts on this blog we have talked about elliptic curves, which are examples of algebraic groups (which is itself a specific instance ...
[1604.01005] Reductive group actions - arXiv
In this paper, we study rationality properties of reductive group actions which are defined over an arbitrary field of characteristic zero.
Reductive Algebraic Groups - Stockholm University
Classification of reductive groups over algebraically closed fields using root data. Geometric construction of representations by the Borel-weil theorem.
The structure of reductive groups - UBC Math
I'll not say anything about the general theory of such groups, but I should say that in practice the specification of an algebraic group is ...
iAG: Algebraic Groups: An introduction to the theory of algebraic group schemes over fields · LAG: Lie Algebras, Algebraic Groups, and Lie Groups · RG: Reductive ...