Geodesic
Biderivations and Commuting Linear Maps on Current Lie Algebras
Journal of Lie theory, Tome 31 (2021) no. 1, pp. 119-126
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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 
@article{JLT_2021_31_1_JLT_2021_31_1_a5,
     author = {D. Eremita},
     title = {Biderivations and {Commuting} {Linear} {Maps} on {Current} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {119--126},
     year = {2021},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2021_31_1_JLT_2021_31_1_a5/}
}
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D. 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/JLT_2021_31_1_JLT_2021_31_1_a5/