Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $K_0$-group of absolute Matrix order unit spaces   In this paper, we describe the Grothendieck group $K_0(V)$ of an absolute
matrix order unit space $V$. For this purpose, we discuss the direct limit of
absolute matrix order unit spaces. We show that $K_0$ is a functor from
category of absolute matrix order unit spaces with morphisms as unital
completely $\vert \cdot \vert$-preserving maps to category of abelian groups.
We study order structure on $K_0(V)$ and prove that under certain condition
$K_0(V)$ is an ordered abelian group. We also show that the functor $K_0$ is
additive on orthogonal unital completely $\vert \cdot \vert$-preserving maps.

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The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con