2024/04/09 by Boris Kunyavskiı̆, Kunyavskii, Boris, Ievgen Makedonskyi +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2404.06045
openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrak g over an algebraically closed field k of characteristic zero, we study the bracket width of current Lie algebras L=\mathfrak g⊗ A. We show that for an arbitrary A the width is at most 2. For A=k[[t]] and A=k[t] we compute the width for algebras of types A and C.