Remarks on Leibniz algebras
Yunhe Sheng, Zhangju Liu
TL;DR
This paper explores the construction of Lie 2-algebras from Leibniz algebras, introduces naive representations to realize algebraic operations concretely, and studies properties of naive cohomologies.
Contribution
It presents a novel method to associate Lie 2-algebras with Leibniz algebras and introduces naive representations and cohomologies.
Findings
Constructed Lie 2-algebras from Leibniz algebras
Defined naive representations for Leibniz algebras
Analyzed properties of naive cohomologies
Abstract
In this paper, first we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. Furthermore, we introduce the notion of the naive representation for a Leibniz algebra in order to realize the abstract operations as a concrete linear operation. At last, we study some properties of naive cohomologies.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models