Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:defines |
A group in which every element is unipotent
|
| gptkbp:example |
Group of upper triangular matrices with 1s on the diagonal
|
| gptkbp:field |
Algebraically closed field
|
| https://www.w3.org/2000/01/rdf-schema#label |
Unipotent group
|
| gptkbp:opposedBy |
gptkb:Reductive_group
|
| gptkbp:property |
All elements have all eigenvalues equal to 1
Closed under group operations Connected in characteristic zero Every element minus the identity is nilpotent Lie algebra consists of nilpotent matrices Normal subgroup of Borel subgroup Solvable Trivial center in some cases Can be represented as a subgroup of GL(n) consisting of unipotent matrices Every unipotent group is nilpotent in characteristic zero |
| gptkbp:relatedTo |
gptkb:Nilpotent_group
|
| gptkbp:studiedIn |
gptkb:Algebraic_geometry
gptkb:Group_theory gptkb:Representation_theory |
| gptkbp:bfsParent |
gptkb:Linear_Algebraic_Groups
gptkb:Algebraic_groups |
| gptkbp:bfsLayer |
7
|