Essays on the structure of reductive groups
نویسنده
چکیده
Here G is considered as an algebraic group defined over F . The Lie algebra g may be identified with Mn(F ), with Lie bracket [X,Y ] = XY − Y X . The group T is isomorphic to the algebraic torus Gm, T (F ) is isomorphic to (F), and the Lie algebra t is isomorphic to F. The character group X(T ) is the lattice of algebraic homomorphisms T → Gm, the cocharacter group that of algebraic homomorphisms Gm → T . These are free Z-modules of rank n, and are canonically dual. I express them additively. If x has diagonal entries xi, we have the characters x 7−→ xi = xi , that make up a basis ofX(T ). The group T (F ) acts by conjugation on g, which decomposes into the direct sum of t and n(n− 1) eigenspaces of dimension one, on which T acts by the multiplicative characters
منابع مشابه
The Effect of Dynamic Assessment of Toulmin Model through Teacher- and Collective-Scaffolding on Argument Structure and Argumentative Writing Achievement of Iranian EFL Learners
Considering the paramount importance of writing logical arguments for college students, this study investigated the effect of dynamic assessment (DA) of Toulmin model through teacher- and collective-scaffolding on argument structure and overall quality of argumentative essays of Iranian EFL university learners. In so doing, 45 male and female Iranian EFL learners taking part in the study were r...
متن کاملEssays on the structure of reductive groups Root systems
SupposeG to be a reductive group defined over an algebraically closed field k. There exist inGmaximal subgroups which are tori, that is to say algebraically isomorphic to a product of copies of k. Fix one of them, say A. The adjoint action of A on g is the direct sum of eigenspaces. The 0-eigenspace is a, and the rest are of dimension one. An eigencharacter λ 6= 0 is called a root of the Lie al...
متن کاملSynthesis of Zinc Dimethyldithiocarbamate by Reductive Disulfide Bond Cleavage of Tetramethylthiuram Disulfide in Presence of Zn2+
The zinc(II) complex [Zn2(dmdtc)2(μ-dmdtc)2] has been synthesized directly from thiram ligand, containing a disulfide bond {dmdtc = N,N-dimethyldithiocarbamate; thiram = N,N-tetramethylthiuram disulfide}, and characterized by elemental analysis and spectroscopic methods. Surprisingly thiram, undergoes a reductive disulfide bond scission upon reaction with Zn2+ in methanolic media to give the [Z...
متن کاملEssays on the structure of reductive groups From root datum to reductive group
A root datum is a quadruple L = (L,∆, L,∆) in which (1) L is a free Z-module of finite rank and L is its dual Hom(L,Z); (2) ∆ is a finite subset of L and ∆ is one of L; (3) implicit is a map α 7→ α from ∆ to∆ such that (〈α, β∨〉) is a Cartan matrix. In the literature, this is usually called a based root datum. For my purposes it serves as a better beginning. I’ll say later something about the di...
متن کاملUsing Writing Checklist in Composing Descriptive Essays Among EFL Learners at the Intermediate Level
This study investigated the impact of writing checklist on composing descriptive essays among EFL learners at the intermediate level. Sixty participants were assigned to experimental and control groups. Both groups were given a pre-test of writing a descriptive essay including 150 words. The experimental group used checklist for learning while the control used teacher correcting technique in ea...
متن کاملEssays on Coxeter groups Bruhat closures
If G is a split reductive group and B a Borel subgroup then G is the disjoint union of the BwB as w ranges over the Weyl group of a maximal torus in B. The closure of BwB is the union of certain double cosets BxB, where the x that occur can be characterized in purely combinatorial terms. Somewhat surprisingly, this combinatorial definition may be extended to define the Bruhat closure operation ...
متن کامل