Lattices are certain discrete subgroups of Lie groups or, more generally, locally compact topological groups. Such a topological group G carries an invariant measure (for Lie groups, the volume form provides an invariant measure). A discrete subgroup \Gamma is a lattice, if there is a subset F of finite volume/measure in G whose \Gamma translates cover all of G. Being a lattice imposes some constraints on the structure an geometry of \Gamma.
The lecture will discuss several important examples in detail, such as arithmetically defined groups like SL_n(Z), which is a lattice SL_n(R).
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| Studiengang/-angebot | Gültigkeit | Variante | Untergliederung | Status | Sem. | LP | |
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| Studieren ab 50 | |||||||
| Studieren ab 50 |