We introduce a notion of a coloured, topologically directed free vector space, which is a vector space viewed as a coloured and topologically directed free graph in a natural sense, to classify finite abelian groups by their group C^*-algebras as vector spaces coloured and topologically directed free in our sense, as the main purpose.

finite abelian group, group C^*-algebra, graph, vector space.

Received: November 2, 2021; Accepted: December 20, 2021; Published: January 14, 2022

How to cite this article: Takahiro Sudo, Vector spaces as coloured, topologically directed-free graphs for finite abelian groups and their C^*-algebras, International Journal of Functional Analysis, Operator Theory and Applications 13(2) (2021), 79-84. DOI: 10.17654/0975291921002

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