Dialgebra Structure of $F[x]\otimes F[x]$, Derivations and Diderivations

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2025年8月9日

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Gabriel Gustavo Restrepo-Sánchez,
José Gregorio Rodríguez-Nieto,
Olga Patricia Salazar-Díaz,
Andrés Sarrazola-Alzate,
Raúl Velásquez

摘要

Let F be a field of zero characteristic. We define a dialgebra structure over the polynomial algebra $F[x] \otimes F[x]$ $F [x] \otimes F [x]$ , and we give a complete classification of the Lie algebra of derivations and the space of diderivations . We also show that the results of this work are closely related to those obtained in Lin and Zhang (Commun Algebra 38(9):3417–3447, 2010) and Restrepo-Sánchez (Inmersión de dialgebras en dialgebras separables, adición de unidades barra y biderivaciones, Tesis de Maestría, Universidad de Antioquia, Medellin, 2010).

Dialgebra Structure of \(F[x]\otimes F[x]\), Derivations and Diderivations

摘要