例句與造句

1. Conversely for any root datum there is a reductive algebraic group.
2. A connected split reductive algebraic group over " K " is uniquely determined ( up to isomorphism ) by its root datum, which is always reduced.
3. The subgroups for which the corresponding homogeneous space has an invariant complex structure correspond to parabolic subgroups in the complexification of the compact Lie group, a reductive algebraic group.
4. Besides the already mentioned connections with the structure of reductive algebraic groups over general and local fields, buildings are used to study their rigidity theorems of George Mostow and Grigory Margulis, and with Margulis arithmeticity.
5. However, there are some exotic pseudo-reductive algebraic groups over non-perfect fields whose construction is related to the construction of Ree groups, as they use the same exotic automorphisms of Dynkin diagrams that change root lengths.
6. It's difficult to find reductive algebraic group in a sentence. 用reductive algebraic group造句挺難的
7. If " G " is a connected reductive algebraic group over the algebraically closed field " K ", then its Langlands dual group " L " " G " is the complex connected reductive group whose root datum is dual to that of " G ".
8. Unlike the Steinberg groups, the Ree groups are not given by the points of a connected reductive algebraic group defined over a finite field; in other words, there is no " Ree algebraic group " related to the Ree groups in the same way that ( say ) unitary groups are related to Steinberg groups.
9. A series of mathematicians applying harmonic analysis to number theory, most notably Martin Eichler, Atle Selberg, Robert Langlands, and James Arthur, have generalised the Poisson summation formula to the Fourier transform on non-commutative locally compact reductive algebraic groups G with a discrete subgroup \ Gamma such that G / \ Gamma has finite volume.
10. If " G " is a reductive algebraic group and P = MAN is the Langlands decomposition of a parabolic subgroup " P ", then parabolic induction consists of taking a representation of MA, extending it to " P " by letting " N " act trivially, and inducing the result from " P " to " G ".
11. Hilbert's fourteenth problem asks whether the ring of invariants is finitely generated or not ( the answer is affirmative if " G " is a reductive algebraic group by Nagata's theorem . ) The finite generation is easily seen for a finite group " G " acting on a finitely generated algebra " R " : since " R " is integral over " R " " G ", the Artin Tate lemma implies " R " " G " is a finitely generated algebra.