Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing isomorphisms between lattices   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. It was shown in previous work that, under
certain hypotheses on A, there exists an algorithm that for a given (left)
Lambda-lattice X either computes a free basis of X over Lambda or shows that X
is not free over Lambda. In the present article, we generalise this by showing
that, under weaker hypotheses on A, there exists an algorithm that for two
given Lambda-lattices X and Y either computes an isomorphism X -> Y or
determines that X and Y are not isomorphic. The algorithm is implemented in
Magma for A=Q[G], Lambda=Z[G] and Lambda-lattices X and Y contained in Q[G],
where G is a finite group satisfying certain hypotheses. This is used to
investigate the Galois module structure of rings of integers and ambiguous
ideals of tamely ramified Galois extensions of Q with Galois group isomorphic
to Q_8 x C_2, the direct product of the quaternion group of order 8 and the
cyclic group of order 2.

12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat