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arXiv · 2101.01966

$K_0$-group of absolute Matrix order unit spaces

Anil Kumar Karn·Amit kumar
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Abstract

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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Anil Kumar Karn, Amit kumar. 2021-01-06. $K_0$-group of absolute Matrix order unit spaces. https://arxiv.org/abs/2101.01966

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