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Polynomial invariants for three-dimensional Leibniz algebras
Part of:
Special aspects of infinite or finite groups
Basic linear algebra
General nonassociative rings
General commutative ring theory
Published online by Cambridge University Press: 25 November 2025
Abstract
For each three-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 three-dimensional non-Lie Leibniz algebras can be distinguished by the traces of degrees 
$\leqslant 2$ and by the dimensions of their automorphism groups.
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society
Footnotes
This work is supported by the FCT 2023.08031.CEECIND, UID/00212/2025, and FAPESP 2023/17918-2.
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