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This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg algebras and their modules. Our results may be regarded as improvements of the attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology theory developed here and some classical problems are pointed out, e.g. extensions of algebras and modules, and deformation… (More)

A family of probability distributions parametrized by an open domain Λ in R n defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix is positive definite defining in this way a Riemannian metric on Λ. If we replace the "positive… (More)

Let us begin by considering two book titles: A provocative title, What Is a Statistical Model? McCullagh (2002) and an alternative title, In a Search for Structure. The Fisher Information. Gromov (2012). It is the richness in open problems and the links with other research domains that make a research topic exciting. Information geometry has both… (More)

Inspired by recent works of Zang Liu, Alan Weinstein and Ping Xu, we introduce the notions of CC algebroids and non asymmetric Courant algebroids and study these structures. It is shown that CC algebroids of rank greater than 3 are the same as Courant algebroids up to a constant factor, though the definition of CC algebroids is much simpler than that of… (More)

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