In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field F, with char(F) different than 2. We describe the main properties of such class of Leibniz algebras and we also compute the biderivations of the four-dimensional Dieudonné Leibniz algebra d1. Eventually we give an algorithm for finding derivations and anti-derivations of a Leibniz algebra as pair of matrices with respect to a fixed basis.
Mancini, M. (2023). Biderivations of Low-Dimensional Leibniz Algebras. In H. Albuquerque, J. Brox, M. Martínez, P. Saraiva (a cura di), Non-Associative Algebras and Related Topics. NAART II, Coimbra, Portugal, July 18–22, 2022 (pp. 127-136). Springer [10.1007/978-3-031-32707-0_8].
Biderivations of Low-Dimensional Leibniz Algebras
Mancini, Manuel
2023-01-01
Abstract
In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field F, with char(F) different than 2. We describe the main properties of such class of Leibniz algebras and we also compute the biderivations of the four-dimensional Dieudonné Leibniz algebra d1. Eventually we give an algorithm for finding derivations and anti-derivations of a Leibniz algebra as pair of matrices with respect to a fixed basis.
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