Search results for "leibniz"
showing 10 items of 18 documents
Obstruction theory in action accessible categories
2013
Abstract We show that, in semi-abelian action accessible categories (such as the categories of groups, Lie algebras, rings, associative algebras and Poisson algebras), the obstruction to the existence of extensions is classified by the second cohomology group in the sense of Bourn. Moreover, we describe explicitly the obstruction to the existence of extensions in the case of Leibniz algebras, comparing Bourn cohomology with Loday–Pirashvili cohomology of Leibniz algebras.
Weakly algebraizable logics
2000
AbstractIn the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.
La voie des idées, de Descartes à Hume
2015
International audience; Lorsque Descartes fait de la connaissance de l'esprit humain la principale tâche de la philosophie, il lui applique l'idée moderne de la science comme connaissance certaine et évidente. Durant les 150 ans qui suivront, aucun penseur ne reniera cette étincelle cartésienne. Dans son sillage mais aussi contre elle, dans le ciel de la philosophie apparaît une constellation de penseurs de premier ordre : Pascal, Hobbes, Spinoza, Malebranche, Leibniz, Locke, Berkeley, Hume. La recherche philosophique accompagnant la "révolution scientifique" commencée avec Galilée s'engage alors dans "la voie des idées". C'est donc sur cette voie que Pierre Guenancia nous entraîne, soulign…
On Internal Relations in Leibniz, British Neo-realism and Whitehead
2011
International audience
Simple Facts Concerning Nambu Algebras
1998
A class of substitution equations arising in the extension of Jacobi identity for $n$-gebras is studied and solved. Graded bracket and cohomology adapted to the study of formal deformations are presented. New identities in the case of Nambu-Lie algebras are proved. The triviality in the Gerstenhaber sense of certain deformed n-skew-symmetric brackets, satisfying the Leibniz rule with respect to a star-product, is shown for n≥ 3.
About Leibniz cohomology and deformations of Lie algebras
2011
We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding whether it has more Leibniz deformations than just the Lie ones. We also give the complete description of a Leibniz (and Lie) versal deformation of the 4-dimensional diamond Lie algebra, and study the case of its 5-dimensional analogue.
"Tout est mal"? Leopardi, Leibniz et la querelle de l'optimisme
2011
National audience
Universal Gravitation and the (Un)Intelligibility of Natural Philosophy
2019
This article centers on Hume's position on the intelligibility of natural philosophy. To that end, the controversy surrounding universal gravitation shall be scrutinized. It is very well known that Hume sides with the Newtonian experimentalist approach rather than with the Leibnizian demand for intelligibility. However, what is not clear is Hume's overall position on the intelligibility of natural philosophy. It shall be argued that Hume declines Leibniz's principle of intelligibility. However, Hume does not eschew intelligibility altogether; his concept of causation itself stipulates mechanical intelligibility. peerReviewed
Two-step nilpotent Leibniz algebras
2022
In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. In particular, we describe the complex and the real case of the indecomposable Heisenberg Leibniz algebras as a generalization of the classical $(2n+1)-$dimensional Heisenberg Lie algebra $\mathfrak{h}_{2n+1}$. Then we use the Leibniz algebras - Lie local racks correspondence proposed by S. Covez to show that nilpotent real Leibniz algebras have always a global integration. As an application, we integrate the indecomposable nilpotent real Leibniz algebras with one-dimensional commutator ideal. We also show that every Lie quandle integr…
Comunità degli spiriti
2014
Il tema leibniziano della società degli spiriti, ovvero di quelle anime razionali che, in quanto capaci di accedere alle verità eterne, si rendono simili a Dio, il tema comunitario del Dio che, proprio in ragione di questa affinità, stringe con gli altri spiriti una società, ripropone per certi versi il motivo classico del legame tra polis e amicizia. Tale motivo conosce però, nel disegno leibniziano di una società degli spiriti, uno slancio nuovo, che si lega alla figura di un Dio non autoreferenziale, di un governante che nel governato riconosce il principio a partire dal quale, solo, si rende visibile la sua stessa bontà.