Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The disappearance of causality at small scale in almost-commutative
  manifolds   This paper continues the investigations of noncommutative ordered spaces put
forward by one of the authors. These metaphoric spaces are defined dually by
so-called \emph{isocones} which generalize to the noncommutative setting the
convex cones of order-preserving functions. In this paper we will consider the
case of isocones inside almost-commutative algebras of the form ${\cal
C}(M)\otimes A_f$, with $M$ a compact metrizable space. We will give a family
of isocones in such an algebra with the property that every possible isocone is
contained in exactly one member of the family. We conjecture that this family
is in fact a complete classification, a hypothesis related with the
noncommutative Stone-Weierstrass conjecture. We also obtain that every isocone
in ${\cal C}(M)\otimes A_f$, with $A_f$ noncommutative, induces an order
relation on $M$ with the property that every point in $M$ lies in a
neighbourhood of incomparable points. Thus, if the causal order relation on
spacetime is induced by an isocone in an almost-commutative (but not
commutative) algebra, then causality must disappear at small scale.

10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph