Geodesic
Biderivations and Commuting Linear Maps on Current Lie Algebras
Daniel Eremita1
1Dept. of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor 2000, Slovenia
Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 119-126

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $L$ be a Lie algebra and let $A$ be an associative commutative algebra with unity, both over the same field $F$. We consider the following two questions. Is every skew-symmetric biderivation on the current Lie algebra $L\otimes A$ of the form $(x,y) \mapsto \lambda([x,y])$ for some $\gamma \in {\rm Cent}(L\otimes A)$, if the same holds true for $L$? Does every commuting linear map of $L\otimes A$ belong to ${\rm Cent}(L\otimes A)$, if the same holds true for $L$?
Classification : 17B05, 17B40, 15A69, 16R60
Mots-clés : Lie algebra, current Lie algebra, tensor product of algebras, biderivation, commuting linear map, centroid

Daniel Eremita  1

1 Dept. of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor 2000, Slovenia 
Daniel Eremita. Biderivations and Commuting Linear Maps on Current Lie Algebras. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 119-126. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a5/
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