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Moufang Patterns and Geometry of Information

Combe, Noémie and Manin, Yuri I. and Marcolli, Matilde (2021) Moufang Patterns and Geometry of Information. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210825-184621604

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Abstract

Technology of data collection and information transmission is based on various mathematical models of encoding. The words "Geometry of information" refer to such models, whereas the words "Moufang patterns" refer to various sophisticated symmetries appearing naturally in such models. In this paper we show that the symmetries of spaces of probability distributions, endowed with their canonical Riemannian metric of information geometry, have the structure of a commutative Moufang loop. We also show that the F-manifold structure on the space of probability distribution can be described in terms of differential 3-webs and Malcev algebras. We then present a new construction of (noncommutative) Moufang loops associated to almost-symplectic structures over finite fields, and use then to construct a new class of code loops with associated quantum error-correcting codes and networks of perfect tensors.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2107.07486arXivDiscussion Paper
Additional Information:Dedicated to Don Zagier. N. C. Combe acknowledges support from the Minerva Fast track grant from the Max Planck Institute for Mathematics in the Sciences, in Leipzig. Yu. Manin acknowledges the continuing strong support from the Max Planck Institute for Mathematics in Bonn. M. Marcolli acknowledges support from NSF grants DMS–1707882 and DMS-2104330.
Funders:
Funding AgencyGrant Number
Max Planck Institute for Mathematics in the SciencesUNSPECIFIED
Max Planck Institute for MathematicsUNSPECIFIED
NSFDMS-1707882
NSFDMS-2104330
Subject Keywords:Probability distributions, convex cones, Moufang loops, quasigroups, Malcev algebras, error–correcting codes, asymptotic bound, code loops, perfect tensors, tensor networks, CRSS quantum codes
Classification Code:MSC 2010 subject classifications: 53D45, 62B10.
Record Number:CaltechAUTHORS:20210825-184621604
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210825-184621604
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110556
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Aug 2021 21:57
Last Modified:25 Aug 2021 22:19

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