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unipotent element
Sign in to saveAlso known as unipotent, unipotency
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.
~9 min read
Encyclopedic overview
17 sectionsContents
- Definition
- Definition with matrices
- Definition with ring theory
- Definition with representation theory
- Examples
- U<sub>''n''</sub>
- G<sub>a</sub><sup>''n''</sup>
- Kernel of the Frobenius
- Classification of unipotent groups over characteristic 0
- Remarks
- Unipotent radical
- Decomposition of algebraic groups
- Characteristic 0
- Characteristic ''p''
- Jordan decomposition
- See also
- References
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.
Excerpted from Wikipedia’s “unipotent element” article, available under the CC BY-SA 4.0 licence.