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Perfect crossed modules in Lie algebras. (English) Zbl 0860.17032
Summary: In the present work we study perfect crossed modules and universal central extensions, which are a generalization of perfect covers in Lie algebras to crossed modules category in Lie algebras, obtaining the following fundamental result: “A crossed module is perfect if and only if it admits a universal central extension”.

MSC:
17B55 Homological methods in Lie (super)algebras
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