On algebras and groups of formal series over a small category, non-abelian stochastic cosurfaces and topological quantum field theories

Jean-Pierre Magnot (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

Based on the example of stochastic cosurfaces, we develop the notion of groups of series indexed by a graded small category, with coefficients in a Fr\"olicher algebra. The presence of the notion of small category is motivated by the cobordism-like relations of stochastic cosurfaces, while the use of Fr\"olicher algebra is a framework adapted to convolution of probabilities. Basic description of these groups, which generalize classical groups of series, is given, and the example raised by non-abelian stochatic cosurfaces of any dimension is studied.MSC(2010): 22E65, 22E66, 58B25, 70G65.

Mots clés: infinite dimensional groups; exponential map; q-deformed operators; cobordism; topological quantum field theories; Stochastic cosurfaces; groups of series; Frölicher algebras

Domaines: Géométrie différentielle [math.DG]; Physique mathématique [math-ph]; Algèbres d'opérateurs [math.OA]; Théorie spectrale [math.SP]; Physique Quantique [quant-ph]

Jean-Pierre Magnot. On algebras and groups of formal series over a small category, non-abelian stochastic cosurfaces and topological quantum field theories. 2020. ⟨hal-01961439v2⟩