Some generalizations of the notion of Lie algebra
Dennise Garc\'ia-Beltr\'an, Jos\'e A. Vallejo
TL;DR
This paper introduces generalized algebraic structures called quasi-Loday algebroids and omni-Loday algebroids, unifying Lie algebroids, omni-Lie algebras, and omni-Loday algebroids within a broader framework.
Contribution
It defines new algebraic concepts and constructs a universal space that encompasses various existing structures, extending the theory of Lie and Loday algebroids.
Findings
Introduction of left and right quasi-Loday algebroids
Construction of a universal omni-Loday algebroid
Unification of Lie algebroids and omni-Lie algebras within a common framework
Abstract
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models