The first condition for the theorem is that the unified group " G contains a subgroup locally isomorphic to the Poincare group . " Therefore the theorem only makes a statement about the unification of the Poincare group with an internal symmetry group.
12.
Local rigidity holds for lattices in semisimple Lie groups providing the latter have no factor of type A1 ( i . e . locally isomorphic to \ mathrm { SL } _ 2 ( \ mathbb R ) ) or the former is irreducible.
13.
Finally one checks that the first of these two extra cases only occurs as a holonomy group for locally symmetric spaces ( that are locally isomorphic to the Cayley projective plane ), and the second does not occur at all as a holonomy group.
14.
In this view, the general procedure for solving an equivalence problem is to construct a system of invariants for the " G "-structure which are then sufficient to determine whether a pair of " G "-structures are locally isomorphic or not.
15.
The Mostow rigidity theorem states that for lattices in simple Lie groups not locally isomorphic to \ mathrm { SL } _ 2 ( \ mathbb R ) ( the group of 2 by 2 matrices with determinant 1 ) any isomorphism of lattices is essentially induced by an isomorphism between the groups themselves.
16.
Mostow rigidity holds ( in its geometric formulation ) more generally for fundamental groups of all complete, finite volume locally symmetric spaces of dimension at least 3, or in its algebraic formulation for all lattices in simple Lie groups not locally isomorphic to \ mathrm { SL } _ 2 ( \ mathbb R ).
17.
:" If G is a simple Lie group not locally isomorphic to \ mathrm { SL } _ 2 ( \ mathbb R ) or \ mathrm { SL } _ 2 ( \ mathbb C ) with a fixed Haar measure and v > 0 there are only finitely many lattices in G of covolume less than v ."
18.
The simplest statement is when \ Gamma is a lattice in a simple Lie group g and the latter is not locally isomorphic to \ mathrm { SL } _ 2 ( \ mathbb R ) or \ mathrm { SL } _ 2 ( \ mathbb C ) and \ Gamma ( this means that its Lie algebra is not that of one of these two groups ).
19.
If X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a "'( G, X )-structure "'on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a ( G, X )-structures are always manifolds and are called "'( G, X )-manifolds " '.
20.
For example, the " p "-torsion of an elliptic curve in characteristic zero is locally isomorphic to the constant elementary abelian group scheme of order " p " 2, but over "'F "'p, it is a finite flat group scheme of order " p " 2 that has either " p " connected components ( if the curve is ordinary ) or one connected component ( if the curve is supersingular ).
How to say locally isomorphic in Hindi and what is the meaning of locally isomorphic in Hindi? locally isomorphic Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
