unipotent वाक्य
उदाहरण वाक्य
मोबाइल
- 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.
- In particular any unipotent group is a nilpotent group, though the converse is not true ( counterexample : the diagonal matrices of GL " n " ( " k " ) ).
- 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.
- Moreover, if " U " is a commutative unipotent group, the exponential map induces an isomorphism from the Lie algebra of " U " to " U " itself.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- This is an example of the unipotent radical of a Borel subgroup ( of the M�bius group, or of SL ( 2, "'C "') for the matrix group; the notion is defined for any reductive Lie group ).
- Ratner's theorems provide a major generalization of ergodicity for unipotent flows on the homogeneous spaces of the form ? \ " G ", where " G " is a Lie group and ? is a lattice in " G ".
- An arbitrary irreducible character has a " Jordan decomposition " : to it one can associate a semisimple character ( corresponding to some semisimple element " s " of the dual group ), and a unipotent representation of the centralizer of " s ".
- By using these holomorphic affine structures we can prove that the period map is affine map into the unipotent orbit of the period domain, and proves a global Torelli theorem for Calabi-Yau type manifolds which asserts that the period maps from the Teichm�ller spaces to the period domains are injective.
- If an epigroup " S " has a partition in unipotent subepigroups ( i . e . each containing a single idempotent ), then this partition is unique, and its components are precisely the unipotency classes defined above; such an epigroup is called " unipotently partionable ".
- More precisely, extensions by algebraic functions correspond to finite differential Galois groups, extensions by integrals correspond to subquotients of the differential Galois group that are 1-dimensional and unipotent, and extensions by exponentials of integrals correspond to subquotients of the differential Galois group that are 1-dimensional and reductive ( tori ).
- The unipotent representations are the trivial representation and the Steinberg representation, and the semisimple representations are all the representations other than the Steinberg representation . ( In this case the semisimple representations do not correspond exactly to geometric conjugacy classes of the dual group, as the center of " G " is not connected .)
- For the special linear group " SL " " n ", the unipotent conjugacy classes are parametrized by partitions of " n " : if " u " is a unipotent element, the corresponding partition is given by the sizes of the Jordan blocks of " u ".
- For the special linear group " SL " " n ", the unipotent conjugacy classes are parametrized by partitions of " n " : if " u " is a unipotent element, the corresponding partition is given by the sizes of the Jordan blocks of " u ".
- As irreducible representations are always "'indecomposable "'( i . e . cannot be decomposed further into a direct sum of representations ), these terms are often confused; however, in general there are many reducible but indecomposable representations, such as the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices.
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