TY - CHAP
AB - We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields. If L is a lattice in the chain and p the prime ideal dividing the index of the lattices in the chain, then the {p}-arithmetic group Aut(L{p}) acts chamber transitively on the corresponding Bruhat-Tits building. So our classification provides a step forward to a complete classification of these chamber transitive groups which has been announced 1987 (without a detailed proof) by Kantor, Liebler and Tits. In fact we find all their groups over number fields and one additional building with a discrete chamber transitive group.
AU - Kirschmer, Markus
AU - Nebe, Gabriele
ID - 42788
SN - 9783319705651
T2 - Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
TI - One Class Genera of Lattice Chains Over Number Fields
ER -