Примеры использования Reductive на Английском языке и их переводы на Русский язык
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A reductive algebraic group over a local field has a BN-pair where B is an Iwahori subgroup.
An Iwahori subgroup is a subgroup of a reductive algebraic group over a nonarchimedean local field that is analogous to a Borel subgroup of an algebraic group.
In seeking to classify reductive groups which need not be split, one step is the Tits index, which reduces the problem to the case of anisotropic groups.
Over perfect fields these are the same as(connected) reductive groups, but over non-perfect fields Jacques Tits found some examples of pseudo-reductive groups that are not reductive. .
Every reductive group over a field admits a central isogeny from the product of a torus
In more detail: an affine group scheme G of finite type over a field k is called linearly reductive if its representations are completely reducible.
Given two reductive groups and a(well behaved)
Reductive groups over an arbitrary field are harder to classify,
A reductive group over a local field has a Tits system(B,
Over local fields this is expected to give a parameterization of L-packets of admissible irreducible representations of a reductive group over the local field.
A reductive group G over a field k is called quasi-split if it contains a Borel subgroup over k.
By contrast, the classification of arbitrary reductive groups can be hard,
Reductive groups include some of the most important groups in mathematics,
Grothendieck showed that split reductive group schemes over any nonempty scheme S are classified by root data.
A reductive group over a field k is called isotropic if it has k-rank greater than 0(that is,
The classification of reductive algebraic groups is in terms of the associated root system,
More generally, a connected linear algebraic group G over an algebraically closed field is called reductive if every smooth connected unipotent normal subgroup of G is trivial.
A central isogeny of reductive groups is a surjective homomorphism with kernel a finite central subgroup scheme.
Reductive mammoplasty is the surgical reduction
Borel subgroups are one of the two key ingredients in understanding the structure of simple(more generally, reductive) algebraic groups, in Jacques Tits' theory of groups with a(B, N) pair.