Applications of Non-commutative Geometry in Associator Theory and Theory of Multiple Zeta Values

Diplôme Thèse Applications of Non-commutative Geometry in Associator Theory and Theory of Multiple Zeta Values eng 2025-06-19 2025-06-19 author Ren Muze 0009-0002-7594-5415 944416 Section de mathématiques (MATH) director Alexeev Anton 134019 Section de mathématiques (MATH) 10.13097/archive-ouverte/unige:186388 urn:nbn:ch:unige-1863888 Sc. 5915 In this thesis, we study the reduced coaction in noncommutative geometry and explore its applications in associator theory and the theory of multiple zeta values. The main results are as follows. We generalize Drinfeld's Knizhinik-Zamolodchikov (KZ) associator theory to paths that start and end at tangential base points that may have a finite number of transversal self-intersections. We derive explicit closed formulas for the reduced coaction maps of open path regularized holonomies of the KZ equation. And explicit formula for the Poisson bracket of matrix entries of regularized holonomies of a pair of loops starting and ending at the same tangential base point. We present a formula that relates the Turaev coaction and the Goncharov–Brown coaction. Motivated by this relation, we introduce the reduced coaction equation. The skew-symmetric solutions to this equation form a Lie algebra under Ihara bracket. Pentagon equation Associator Turaev coaction Reduced coaction Lie algebra Dewey 510 25 Section de mathématiques 11 false 31f39c29-bb9a-4a25-8def-a7b198d90718 Thesis Public Thesis_Muze_Ren-1.pdf 1313059 application/pdf CC BY-4.0 49f80d97e572722d8f7edbcddb2db59ec874c1df19ec82cfb38cbc175d3a65ad e2282248-3651-462d-94ec-1666713bd265 Imprimatur Public impritutor.pdf 719484 application/pdf 1e0993e3f98c8e987242189ba32734e28878d8bdd8c526e161e4bde96dad32cb openAccess Faculté des sciences / Section de mathématiques

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Applications of Non-commutative Geometry in Associator Theory and Theory of Multiple Zeta Values				2025	186	1,327

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