Related papers: Three case studies in current Leibniz scholarship
We study the impact of Lorentz violating terms on a physical observable for both electrodynamics of chiral matter and an Abelian Higgs-like model in $3+1$ dimensions. Our calculation is done within the framework of the gauge-invariant, but…
In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…
We study the problem of the infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first…
During the querelle des infiniment petits, Leibniz wrote several texts to justify using Differential calculus among Parisian savants. However, only three were published. Among these publications, ''Sentiment de Monsieur Leibnitz'' had a…
The paper is devoted studying solvable Leibniz algebras with a nilradical possessing the codimension equals the number of its generators. We describe this class in non-split nilradical case. Then the case of split nilradical is worked out.…
We give a survey of current research on G\"{o}del's incompleteness theorems from the following three aspects: classifications of different proofs of G\"{o}del's incompleteness theorems, the limit of the applicability of G\"{o}del's first…
We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.
The idea that quantum gravity manifestations would be associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. Other related ideas seem to be drowning in interpretational…
We first present a review, intended for classical relativists, of the ultraviolet difficulties faced by local quantum gravity theories in both the usual Einstein versions and in their supergravity extensions, at least perturbatively. These…
We study the algebras of derivations of nilpotent Leibniz algebras of low dimensions.
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on…
We perform a thorough investigation of Lifshitz-like metrics with hyperscaling violation (hvLif) in four-dimensional theories of gravity coupled to an arbitrary number of scalars and vector fields, obtaining new solutions, electric,…
The problematic relationship between science and philosophy has, since the beginning of modernity, divided the world into two separate domains: nature and human. Some of today's schools of philosophy and epistemological inquiry have…
We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of…
A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizeable; that is, if all 2-generated subalgebras are…
In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebra. We give specific descriptions of those Leibniz algebras…
In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are…
QBism is a novel interpretation of quantum mechanics. With its radical emphasis on the subject, QBism provides a welcome corrective to popular misrepresentations of the epistemological reflections of Niels Bohr, while Bohr, rightly…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…