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dw invariant

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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EXPLICIT cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf–Witten invariants
Part of
Hua-Lin Huang, Zheyan Wan, Yu Ye
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 4 / August 2020

Published online by Cambridge University Press:

13 March 2019, pp. 1937-1964

Print publication:

August 2020
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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.