Computing isomorphisms between lattices

Henri Johnston (University of Exeter)

Wednesday 27th March, 2019 16:00-17:00 Maths 311B


Let K be a number field, let A be a finite dimensional
semisimple K-algebra and let Lambda be an O_K-order in A. In particular,
for a finite group G, one can take A=Q[G] and Lambda=Z[G]. In this talk,
we shall describe an algorithm that, under certain hypotheses on A, for
two given Lambda-lattices X and Y either computes an isomorphism X -> Y
or determines that X and Y are not isomorphic. This algorithm can be
used to investigate questions concerning the Galois module structure of
rings of integers and ambiguous ideals of tamely ramified Galois
extensions of Q. This is joint work with Tommy Hofmann (Kaiserslautern).

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