Another group of phenomena concerning lattices in semisimple algebraic groups is collectively known as rigidity. The Mostow rigidity theorem showed that the algebraic structure of a lattice in simple Lie group G of split rank at least two determines G. Thus any isomorphism of lattices in two such groups is essentially induced by an isomorphism between the groups themselves. Superrigidity provides a generalization dealing with homomorphisms from a lattice in an algebraic group G into another algebraic group H.
Read more about this topic: Lattice (discrete Subgroup)
Famous quotes containing the word rigidity:
“[University students] hated the hypocrisy of adult society, the rigidity of its political institutions, the impersonality of its bureaucracies. They sought to create a society that places human values before materialistic ones, that has a little less head and a little more heart, that is dominated by self-interest and loves its neighbor more. And they were persuaded that group protest of a militant nature would advance those goals.”
—Muriel Beadle (b. 1915)