Search results for " Leibniz"
showing 5 items of 5 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.
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…
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.
Leibniz, l’individuo, l’Europa: Kurt Huber – Die Weisse Rose
2022
This contribution is dedicated to the figure of Kurt Huber, one of the protagonists of the anti-Nazi resistance group of the White Rose, and to the studies he dedicated to the thought of Leibniz. The great German philosopher, investigated in the link that binds monadology to the thought of individuality, appears as a source for rethinking the relationship between Germany and Europe and for overcoming Nazi barbarism.