Journal of Lie Theory

no. 1
Biderivations and Commuting Linear Maps on Current Lie Algebras
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 119-126
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 $L$?
DOI: 10.5802/jolt.1161
Classification: 17B05, 17B40, 15A69, 16R60
Keywords: Lie algebra, current Lie algebra, tensor product of algebras, biderivation, commuting linear map, centroid 
@article{JOLT_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},
     doi = {10.5802/jolt.1161},
     zbl = {1475.17011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1161/}
}
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D. Eremita. Biderivations and Commuting Linear Maps on Current Lie Algebras. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 119-126. doi: 10.5802/jolt.1161

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