Semi-Cosimplicial Hilbert Spaces with Isometric Coface Operators

Summary · qwen2.5:32b

The article introduces and develops semi-cosimplicial Hilbert spaces with isometric coface operators, linking to non-commutative probability theory through the concept of spreadability. This work explores applications in areas such as cohomology, representation theory, and graph decomposition, offering a new framework for understanding distributional symmetry. A key detail involves the classification and extensions of semi-cosimplicial sets with injective coface maps, providing foundational insights into their structure and potential theoretical applications.

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Exploring the intricate world of Semi-Cosimplicial Hilbert Spaces in non-commutative probability theory.

Excerpt

arXiv:2603.27373v2 Announce Type: replace Abstract: Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically developed in various directions: partial shifts, cohomology, Hessenberg form, a related graph, decomposition into labeled subspaces, representation theory of the infinite symmetric and braid groups, classification and extensions for semi-cosimplicial sets with injective coface maps and a toy version of spreadability.