On the commutativity degree of a finite-dimensional Lie algebra
Afsaneh Shamsaki, Ahmad Erfanian, Mohsen Parvizi
TL;DR
This paper introduces the concept of commutativity degree for finite-dimensional Lie algebras over finite fields, establishing bounds and exploring its relation to existing Lie algebra concepts.
Contribution
It defines the commutativity degree for these Lie algebras and provides bounds and relations to known algebraic properties, advancing understanding of their structure.
Findings
Established upper and lower bounds for the commutativity degree.
Connected the commutativity degree to existing Lie algebra concepts.
Provided insights into the structure of finite-dimensional Lie algebras.
Abstract
In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known concepts in Lie algebras.
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 · Advanced Algebra and Geometry · Finite Group Theory Research