Analytic density in Lie groups |
| |
Authors: | Richard D Mosak Martin Moskowitz |
| |
Institution: | (1) Department of Mathematics and Computer Science, Herbert H. Lehman College, CUNY, 10468 Bronx, NY, USA;(2) Department of Mathematics, Graduate Center CUNY, 10036 New York, NY, USA |
| |
Abstract: | A subgroupH of an analytic groupG is said to beanalytically dense if the only analytic subgroup ofG containingH isG itself. The main purpose of this paper is to give sufficient conditions onG (analogous to those of 8], 9], and 7] in the case of Zariski density) which guarantee the analytic density of cofinite
volume subgroupsH. First we consider the case of arbitrary cofinite volume subgroups (Theorem 5 and its corollaries). Then we specialize to
lattices, and prove the following result (Theorem 8):Let G be an analytic group whose radical is simply connected and whose Levi factor has no compact part and a finite center.
Then any lattice in G is analytically dense. In proving this use is made of a result of Montgomery which also implies that for any simply connected solvable group, cocompactness
of a closed subgroup implies analytic density. In the case of a solvable group with real roots this means analytic density
and cocompactness are equivalent and thus completes a circle of ideas raised in Saito 13]. In Corollary 9 we deal with a
related local condition. Finally in Theorem 10 and its corollaries we apply these considerations to prove a homomorphism extension
theorem and an isomorphism theorem for 1-dimensional cohomology. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|