The first braided homology group (Q2785919)

This paper is devoted to the study of a braided version of Chevalley-Eilenberg cohomology. First, the authors recall the basic definitions of braided categories, algebras and Lie algebras in a braided category, and their modules. Next, they show that for certain modules over a braided Lie algebra there is a braided version of Chevalley-Eilenberg cohomology. Finally, they show that the tensor product of a braided Lie algebra \({\mathfrak g}\) with a braided commutative algebra \(A\) is again a braided Lie algebra and compute the braided cohomology of \({\mathfrak g}\otimes A\) with coefficients in certain modules in terms of braided cohomology of \({\mathfrak g}\) and braided Hochschild cohomology of \(A\).NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].