In the classification of finite simple groups, there is a major division between group of characteristic 2 type, where involutions resemble unipotent elements, and other groups, where involutions resemble semisimple elements.
22.
In particular any unipotent group is a nilpotent group, though the converse is not true ( counterexample : the diagonal matrices of GL " n " ( " k " ) ).
23.
If a unipotent group acts on an affine variety, all its orbits are closed, and if it acts linearly on a finite-dimensional vector space then it has a non-zero fixed vector.
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Moreover, if " U " is a commutative unipotent group, the exponential map induces an isomorphism from the Lie algebra of " U " to " U " itself.
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In fact one of the choices for \ mathfrak { H } has the same characteristic polynomial " X " 2 " 2 " X " + 1 as the identity matrix, and is therefore unipotent.
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Unipotent groups over an algebraically closed field of any given dimension can in principle be classified, but in practice the complexity of the classification increases very rapidly with the dimension, so people tend to give up somewhere around dimension 6.
27.
Informally, Langlands philosophy suggests that there should be a correspondence between representations of a reductive group and conjugacy classes a Langlands dual group, and the unipotent representations should be roughly the ones corresponding to unipotent classes in the dual group.
28.
Informally, Langlands philosophy suggests that there should be a correspondence between representations of a reductive group and conjugacy classes a Langlands dual group, and the unipotent representations should be roughly the ones corresponding to unipotent classes in the dual group.
29.
Red blood cells or " erythrocytes ", primarily carry oxygen and collect carbon dioxide through the use of haemoglobin, and have a lifetime of about 120 days . In the process of being formed they go through a unipotent stem cell stage.
30.
Let G be the general linear group { \ rm GL } _ n, \ psi a smooth complex valued non-trivial additive character of F and U the subgroup of { \ rm GL } _ n consisting of unipotent upper triangular matrices.
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