Groupoid G-spans and matrices over group rings
Joachim Kock, Jesper M. M{\o}ller
TL;DR
This paper introduces G-spans of groupoids and their matrices over group rings, demonstrating that span composition aligns with matrix multiplication when G is a finite abelian group.
Contribution
It defines G-spans of groupoids and establishes a correspondence between span composition and matrix multiplication over group rings for finite abelian groups.
Findings
G-spans of groupoids are formally defined.
Matrices over group rings are associated with G-spans.
Composition of spans corresponds to matrix multiplication.
Abstract
When G is a finite abelian group, we define G-spans of groupoids and their associated matrices with entries in the group ring QG and show that composition of spans corresponds to multiplication of matrices.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Advanced Operator Algebra Research