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Title: Algorithmic enumeration of quaternionic lattices
Author: Chisholm, Sarah
Advisor: Bauer, Mark
Greenberg, Matthew
Keywords: Education--Mathematics
Issue Date: 8-Oct-2014
Abstract: In this thesis, we develop and implement an algorithm in Magma for enumerating isometry classes of quaternionic lattices. This algorithm can be viewed as a higher rank generalization of that used for enumerating equivalence classes of left-ideals of quaternionic orders. Our key technical innovation is an adaptation of Kneser’s method of neighbours to the setting of quaternionic lattices. Central to this adaptation is the Morita equivalence between Hermitian spaces over the split quaternion algebra M2(F) and symplectic spaces over F.
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