In cell biology, a unipotent cell is the concept that one stem cell has the capacity to differentiate into only one cell type.
12.
Over the real numbers ( or more generally any field of characteristic 0 ) the exponential map takes any nilpotent square matrix to a unipotent matrix.
13.
Let " u P " be the dimension of the unipotent group and " t P " the dimension of the torus.
14.
An epigroup is unipotently partionable iff it contains no subsemigroup that is an ideal extension of an unipotent epigroup by " B 2 ".
15.
Any unipotent algebraic group is isomorphic to a closed subgroup of the group of upper triangular matrices with diagonal entries 1, and conversely any such subgroup is unipotent.
16.
Any unipotent algebraic group is isomorphic to a closed subgroup of the group of upper triangular matrices with diagonal entries 1, and conversely any such subgroup is unipotent.
17.
The study of the properties of unipotent and quasiunipotent flows on homogeneous spaces remains an active area of research, with applications to further questions in the theory of Diophantine approximation.
18.
For example, parabolic transformations are conjugate to rigid translations in the upper half-space model, and they are exactly those transformations that can be represented by unipotent upper triangular matrices.
19.
This result follows from the more technical version of the Kazhdan Margulis theorem and the fact that only unipotent elements can be conjugated arbitrarily close ( for a given element ) to the identity.
20.
The concept of reductive is not quite the same for Lie groups as it is for algebraic groups because a reductive Lie group can be the group of real points of a unipotent algebraic group.
