Generalized derivations of current Lie algebras

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 question. Is every generalized derivation (resp. quasiderivation) of L ⊗ A the sum of a derivation and a map from the centroid of L ⊗ A , if the same holds true fo...

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Bibliographic Details
Published in:Communications in algebra 2024-11, Vol.52 (11), p.4603-4611
Main Authors: Benkovič, Dominik, Eremita, Daniel
Format: Article
Language:English
Subjects:
Algebra
Centroids
Current Lie algebra
Derivation
generalized derivation
Lie algebra
Lie groups
quasiderivation
tensor product of algebras
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Summary: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 question. Is every generalized derivation (resp. quasiderivation) of L ⊗ A the sum of a derivation and a map from the centroid of L ⊗ A , if the same holds true for L?
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2354423