Explicit cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf-Witten invariants

Abstract

We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution for any given finite abelian group. With a help of the obtained cocycle formulas, we determine all the braided linear Gr-categories and compute the Dijkgraaf-Witten Invariants of the $n$-torus for all $n$.

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Cited by in corpus (2)

• Symmetry-resolved entanglement in symmetry-protected topological phases
• Finite $p$-groups of class $2$ as central extensions