Year: 2026
Type: preprint
Abstract: We establish and explore the correspondence between positive functionals and cocycles in higher unitary cohomology. We generalize the classical cocycle version of the Gelfand-Naimark-Segal construction to higher degrees and apply it to characterize vanishing of higher unitary cohomology as an extension property for positive functionals. We also prove that under mild conditions the algebraic spectral gap for the one sided Laplacian characterizes cohomological vanishing instead of reducedness of unitary cohomology
Source: arXiv (Cornell University)
Authors: Neumann, Antonio López, Nowak, Piotr W.
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140212876
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