Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cohomology and K-theory of the projective unitary groups PU(n)   The projective unitary group PU(n) is the group of holomorphic isometries on
the complex projective space of dimension n-1. It is essential to the pure
Yang-Mills gauge theory, and to the twisted K-theory. Based on the arithmetic
and combinatorial properties of the prime factorization of the integer n, we
construct the integral cohomology and topological K-theory of the group PU(n),
using generators fashioned from the Weyl invariants of the unitary group U(n).
Applications to the homotopy and representation theory of the group PU(n) are
also discussed.

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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an