Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kummer structures   Suppose we take an abelian group G and quotient it by the action of negation.
What structure does the quotient K inherit from the group structure of G? We
describe this structure (which we call the Kummer of G) in terms of a map from
the set of unordered pairs of elements of K to itself. We propose some axioms
that hold for such structures, and show that every structure satisfying those
axioms either is the Kummer of a unique group, or comes from one other
construction, the quotient of a 2-torsion group by an involution.

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org