Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Roots of unity in definite quaternion orders   A commutative order in a quaternion algebra is called selective if it is
embeds into some, but not all, the maximal orders in the algebra. It is known
that a given quadratic order over a number field can be selective in at most
one indefinite quaternion algebra. Here we prove that the order generated by a
cubic root of unity is selective for any definite quaternion algebra over the
rationals with a type number 3 or larger. The proof extends to a few other
closely related orders.

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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph