Polynomial invariants for 3-dimensional Leibniz algebras

2025/05/11 by Ivan Kaygorodov, Kaygorodov, Ivan, Artem Lopatin +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2505.07125

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each 3-dimensional non-Lie Leibniz algebra over the complex numbers, we describe the algebra of polynomial invariants and determine its group of automorphisms. As a consequence, we establish that any two non-nilpotent 3-dimensional non-Lie Leibniz algebras can be distinguished by the traces of degrees \leqslant 2 and by the dimensions of their automorphism groups.

Citations

• Polynomial invariants for low dimensional algebras
• Novikov algebras in low dimension: identities, images and codimensions
• Symplectic structure, product structures and complex structures on Leibniz algebras
• Polynomial identities and images of polynomials on null-filiform Leibniz algebras
• Cohomology of solvable Leibniz algebras
• Classification of five-dimensional symmetric Leibniz algebras
• Complete Leibniz Algebras
• Invariants of G₂ and Spin(7) in positive characteristic
• Leibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces
• Universal enveloping algebras of Leibniz algebras and (co)homology
• The invariant theory of n × n matrices

Related

• Some three-dimensional non-nilpotent Leibniz algebras: automorphism groups
• Polynomial Identities and Codimensions of Two- and Three-Dimensional Metabelian Non-Lie Leibniz Algebras
• On the automorphism groups of some nilpotent 3-dimensional Leibniz algebras
• Nilpotent Lie and Leibniz algebras
• Automorphism groups of some 3-dimensional Leibniz algebras