3,793 research outputs found
Some generalizations of the notion of Lie algebra
We introduce the notion of left (and right) quasi-Loday algebroids and a
"universal space" for them, called a left (right) omni-Loday algebroid, in such
a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are
particular substructures.Comment: Second version. 14 pages. Included some comments about previous works
related to Leibniz algebras, and updated bibliography. A new example adde
Flat 3-webs of degree one on the projective plane
The aim of this work is to study global -webs with vanishing curvature. We
wish to investigate degree foliations for which their dual web is flat. The
main ingredient is the Legendre transform, which is an avatar of classical
projective duality in the realm of differential equations. We find a
characterization of degree foliations whose Legendre transform are webs
with zero curvature.Comment: 14 page
On Lie Algebroids and Poisson Algebras
We introduce and study a class of Lie algebroids associated to faithful
modules which is motivated by the notion of cotangent Lie algebroids of Poisson
manifolds. We also give a classification of transitive Lie algebroids and
describe Poisson algebras by using the notions of algebroid and Lie
connections
Metastability of non-reversible mean-field Potts model with three spins
We examine a non-reversible, mean-field Potts model with three spins on a set
with points. Without an external field, there are three
critical temperatures and five different metastable regimes. The analysis can
be extended by a perturbative argument to the case of small external fields. We
illustrate the case of large external fields with some phenomena which are not
present in the absence of external field.Comment: 34 pages, 12 figure
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