F-manifolds and geometry of information
| Autor: | Noémie Combe, Yuri I. Manin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Tangent Algebraic geometry 01 natural sciences Mathematics - Algebraic Geometry Analytic geometry Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Probability distribution 0101 mathematics Quantum field theory Algebraic number Algebraic Geometry (math.AG) Commutative property Associative property Mathematics |
| Zdroj: | Bulletin of the London Mathematical Society |
| Popis: | The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since 1990's. The focus of this paper consists in the demonstration that various spaces of probability distributions defined and studied at least since 1960's also carry natural structures of $F$-manifolds. This fact remained somewhat hidden in various domains of the vast territory of models of information storing and transmission that are briefly surveyed here. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|