On braided homology (Q2785937)

In this paper, the authors study cohomology of algebras and Lie algebras in braided categories. First, they recall the main notions from the theory of braided categories, algebras, and Lie algebras in such categories and their modules. Next, they discuss the braided version of Chevalley-Eilenberg cohomology and show that for certain modules the invariants form an acyclic subcomplex of the braided Chevalley-Eilenberg complex. Moreover, they compute the third cohomology of the invariant subcomplex of the exterior algebra of a braided Lie algebra. NEWLINENEWLINENEWLINEFinally, the authors define a braided version of dihedral cohomology and show how this can be applied to compute the braided Chevalley-Eilenberg cohomology of the tensor product of a braided Lie algebra with a braided commutative algebra.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].