2021/09/28 by N. C. Combe, Combe, N. C., P. G. Combe +3
Chemistry · Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Computational Drug Discovery Methods #Differential Geometry (math.DG) #FOS: Mathematics #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.2109.13605
arxiv created 2021/09/28 · openalex publication_date 2021/09/28 · arxiv updated 2021/09/29 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28
Recently, it has been shown that the statistical manifold, related to exponential families, has a Frobenius manifold structure and appears as the fourth class of Frobenius manifolds. It has a structure of a projective manifold over a rank two Frobenius algebra \frakA, being the algebra of paracomplex numbers and generated by 1, ε such that ε2=1. This result is a key step towards an algebraization of the results concerning the manifold of probability distributions and thus offers a new perspective on it. In this paper, we prove that the fourth Frobenius manifold is decomposed into a pair of symmetric totally geodesic pseudo-Riemannian submanifolds, each of which correspond to a module over an ideal of \frakA. This pair of ideals are othogonal idempotents. The symmetry is obtained under the Peirce mirror.