Work

Bracket width of current Lie algebras

Year: 2025

Type: article

Abstract: The length of an element z of a Lie algebra L is defined as the smallest number s needed to represent z as a sum of s brackets. The bracket width of L is defined as supremum of the lengths of its elements. Given a finite-dimensional simple Lie algebra g over an algebraically closed field k of characteristic zero, we study the bracket width of current Lie algebras L = g ⊗ A . We show that for an arbitrary A the bracket width is at most 2. For A = k [ [ t ] ] and A = k [ t ] we compute the bracket width for algebras isomorphic to sl n and sp 2 n .

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.03.023

Authors: Boris Kunyavskii, Ievgen Makedonskyi, Andriy Regeta

Institutions: Bar-Ilan University, Beijing Institute of Mathematical Sciences and Applications, Friedrich Schiller University Jena

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Deutsche Forschungsgemeinschaft, Bar-Ilan University, Israel Science Foundation