F‐Manifolds and geometry of information
Copyright policy )F‐Manifolds and geometry of information
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.
- Max Planck Society Germany
statistical manifolds, weak Frobenius manifolds, projective space, Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.), paracomplex structures, Jordan algebra, probability distributions, Statistical aspects of information-theoretic topics, Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, formally real algebras, Quantum Algebra (math.QA), Classical or axiomatic geometry and physics, Global differential geometry, Algebraic Geometry (math.AG)
statistical manifolds, weak Frobenius manifolds, projective space, Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.), paracomplex structures, Jordan algebra, probability distributions, Statistical aspects of information-theoretic topics, Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, formally real algebras, Quantum Algebra (math.QA), Classical or axiomatic geometry and physics, Global differential geometry, Algebraic Geometry (math.AG)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).9 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!