Algorithmic enumeration of quaternionic lattices

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ucalgary_2014_chisholm_sarah.pdf(503.72 KB)
Date
2014-10-08
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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 Kneserā€™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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Education--Mathematics
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Chisholm, S. (2014). Algorithmic enumeration of quaternionic lattices (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24766
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http://hdl.handle.net/11023/1920
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