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...

&0&*\end{array}}\right)} . The group U {\displaystyle U} is an example of a unipotent linear algebraic group, the group B {\displaystyle B} is an example of...

In mathematics, a unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups...

the capacity to differentiate into only one cell type, meaning they are unipotent stem cells. In embryology, precursor cells are a group of cells that later...

containing it, both invariant under the Frobenius map F, and write U for the unipotent radical of B. If we choose a representative w′ of the normalizer N(T)...

The myeloblast is a unipotent stem cell which differentiates into the effectors of the granulocyte series. It is found in the bone marrow. Stimulation...

largest smooth connected unipotent normal subgroup of G {\displaystyle G} is trivial. This normal subgroup is called the unipotent radical and is denoted...

Ratner's theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner around 1990. The theorems...

subgroup of unipotent elements in the radical is called the unipotent radical, it serves to define reductive groups. Reductive group Unipotent group "Radical...

unipotent cell is the concept that one stem cell has the capacity to differentiate into only one cell type. It is currently unclear if true unipotent...

that every such is (essentially) a semidirect product of a unipotent group (its unipotent radical) with a reductive group. In turn reductive groups are...

the variety of nilpotent elements in a semisimple Lie algebra, or the unipotent elements of a reductive algebraic group, introduced by Tonny Albert Springer...

to an isomorphism, is uniquely determined by V. A representation of a unipotent group is generally not semisimple. Take G {\displaystyle G} to be the...

becomes a common myeloid progenitor or a multipotent stem cell, then a unipotent stem cell, then a pronormoblast (also commonly called an proerythroblast...

proportion of the first order term. Idempotent element (ring theory) Unipotent Reduced ring Nil ideal Nilpotent matrix Polcino Milies & Sehgal (2002)...

They exist to replenish rapidly lost cell types and are multipotent or unipotent, meaning they only differentiate into a few cell types or one type of...

short-term regeneration capacities and committed multipotent, oligopotent, and unipotent progenitors. Hematopoietic stem cells constitute 1:10,000 of cells in...

researchers do not consider multipotency to be essential and believe that unipotent self-renewing stem cells can exist. These properties can be illustrated...

precursor cell, in cytology, a type of partially differentiated, usually unipotent cell Blast disease, a disease of cereal crops Blast injury, a complex...

satisfies the identity xy ≡ yx Idempotent If it satisfies the identity xx ≡ x Unipotent If it satisfies the identity xx ≡ yy Zeropotent If it satisfies the identities...

theory. Around 1990, she proved a group of major theorems concerning unipotent flows on homogeneous spaces, known as Ratner's theorems. Ratner was elected...

demonstrated through clonal analysis that most radial glia have restricted, unipotent or multipotent, fates. Radial glia can be found during the neurogenic...

schemes. Over an algebraically closed field of characteristic 0, any unipotent abelian connected algebraic group is isomorphic to a product of copies...

develops into unipotent cells that will later on form a population of granulocytes, as well as a population of monocytes. The first unipotent cell in granulopoiesis...

geodesic curvature 1 at every point. Every horocycle is the orbit of a unipotent subgroup of PSL(2,R) in the hyperbolic plane. Moreover, the displacement...

In representation theory, a branch of mathematics, θ10 is a cuspidal unipotent complex irreducible representation of the symplectic group Sp4 over a finite...

affine algebraic group defined over k whose k-unipotent radical (i.e., largest smooth connected unipotent normal k-subgroup) is trivial. Over perfect fields...

variations of the group: a discrete version, a pro-l version, a k-pro-unipotent version, and a profinite version; the first three versions were defined...

subgroups of exceptional algebraic groups (1999) Centres of centralizers of unipotent elements in simple algebraic groups (2011) Group Representation Theory...

to molt into either reproductive or non-reproductive phenotypes), to unipotent (able to molt into developmentally close phenotypes), and then finally...