In mathematics, a unipotent element r of a ring R is one such that r − 1 is a nilpotent element; in other words, (r − 1)n is zero for some n.In particular, a square matrix M is a unipotent matrix if and only if its characteristic polynomial P(t) is a power of t − 1. Thus all the eigenvalues of a unipotent matrix are 1.The term quasi-unipotent means that some power is unipotent, for example for a diagonalizable matrix with eigenvalues that are all roots of unity.In the theory of algebraic groups, a group element is unipotent if it acts unipotently in a certain natural group representation. A unipotent affine algebraic group is then a group with all elements unipotent.DefinitionDefinition with matrices
Consider the group \mathbb{U}_n of upper-triangular matrices with 1's along the diagonal, so they are the group of matrices
:\mathbb{U}_n = \left{
\begin{bmatrix}
1 & * & \cdots & * &
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
In mathematics, 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 reductive if it has a represen
In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example i
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the
Let u be a unipotent element of a simple algebraic group G over a field k of characteristic p. We develop a method for computing the connected component of Z(C-G(u)) in the cases where p is positive and both it and the rank of G are small enough. The method is then carried out for G of type G(2), F-4 and E-6 in bad characteristic. (C) 2013 Elsevier Inc. All rights reserved.
Let u be a unipotent element of a simple algebraic group G over a field k of characteristic p. We develop a method for computing the connected component of Z(CG(u)) in the cases where p is positive and both it and the rank of G are small enough. The method is then carried out for G of type G2, F4 and E6 in bad characteristic.
The aim of the course is to give an introduction to linear algebraic groups and to give an insight into a beautiful subject that combines algebraic geometry with group theory.
This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using scheme theory and modern algebraic geometry.