**Unipotent**

In mathematics, a **unipotent element** *r* of a ring *R* is one such that *r* − 1 is a nilpotent element, in other words such that some power (*r* − 1)*n* is zero.

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. Equivalently, *M* is unipotent if all its eigenvalues 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.

A **unipotent affine algebraic group** is one all of whose elements are unipotent (see below for the definition of an element being unipotent in such a group).

Read more about Unipotent: Unipotent Algebraic Groups, Unipotent Radical, Jordan Decomposition

### Other articles related to "unipotent":

**Unipotent**- Jordan Decomposition

... over a perfect field can be written uniquely as the product g = gugs of commuting

**unipotent**and semisimple elements gu and gs ... linear algebraic group over a perfect field is the product of a

**unipotent**group and a semisimple group ...

Springer Correspondence - Example

... For the special linear group SLn, the

... For the special linear group SLn, the

**unipotent**conjugacy classes are parametrized by partitions of n if u is a**unipotent**element, the corresponding partition is given by the ... of the Weyl group corresponds to the regular**unipotent**class, and the sign representation corresponds to the identity element of G) ...Reductive Group

... group is an algebraic group G over an algebraically closed field such that the

... group is an algebraic group G over an algebraically closed field such that the

**unipotent**radical of G is trivial (i.e ... the group of**unipotent**elements of the radical of G) ... algebraically closed, a reductive group is a smooth affine algebraic group such that the**unipotent**radical of G over the algebraic closure is trivial ...Ratner's Theorems

... are a group of major theorems in ergodic theory concerning

... are a group of major theorems in ergodic theory concerning

**unipotent**flows on homogeneous spaces proved by Marina Ratner around 1990 ... The study of the dynamics of**unipotent**flows played a decisive role in the proof of the Oppenheim conjecture by Grigory Margulis ... theorems have guided key advances in the understanding of the dynamics of**unipotent**flows ...Deligne–Lusztig Theory - Lusztig's Classification of Irreducible Characters - Jordan Decomposition

... An irreducible character is called

... An irreducible character is called

**unipotent**if it occurs in some R1T, and is called semisimple if its average value on regular**unipotent**elements is non-zero (in which case the average value is 1 or ... character (corresponding to some semisimple element s of the dual group), and a**unipotent**representation of the centralizer of s ... of the irreducible character is the product of the dimensions of its semisimple and**unipotent**components ...Main Site Subjects

Related Subjects

Related Phrases

Related Words