Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two types of Lie Groups as 4-dimensional Riemannian manifolds with
  circulant structure   A 4-dimensional Riemannian manifold equipped with an endomorphism of the
tangent bundle, whose fourth power is the identity, is considered. The matrix
of this structure in some basis is circulant and the structure acts as an
isometry with respect to the metric. Such manifolds are constructed on
4-dimensional real Lie groups with Lie algebras of two remarkable types. Some
of their geometric characteristics are obtained.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg