Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total Operators and Inhomogeneous Proper Values Equations   Kaehler's two-sided angular momentum operator, K + 1, is neither
vector-valued nor bivector-valued. It is total in the sense that it involves
terms for all three dimensions. Constant idempotents that are "proper
functions" of K+1's components are not proper functions of K+1. They rather
satisfy "inhomogeneous proper-value equations", i.e. of the form (K + 1)U =
{\mu}U + {\pi}, where {\pi} is a scalar. We consider an equation of that type
with K+1 replaced with operators T that comprise K + 1 as a factor, but also
containing factors for both space and spacetime translations. We study the
action of those T's on linear combinations of constant idempotents, so that
only the algebraic (spin) part of K +1 has to be considered. {\pi} is now, in
general, a non-scalar member of a Kaehler algebra. We develop the system of
equations to be satisfied by the combinations of those idempotents for which
{\pi} becomes a scalar. We solve for its solutions with {\mu} = 0, which
actually also makes {\pi} = 0: The solutions with {\mu} = {\pi} = 0 all have
three constituent parts, 36 of them being different in the ensemble of all such
solutions. That set of different constituents is structured in such a way that
we might as well be speaking of an algebraic representation of quarks. In this
paper, however, we refrain from pursuing this identification in order to
emphasize the purely mathematical nature of the argument.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: adap-org