This is a survey of some notions and results related to the cohomology of Lie algebras, motivated by or having applications in physics. Though being far from describing the subject fully, it gives a nice interesting account of some particular topics.
The authors start by introducing all needed notions – mainly cohomology of Lie algebras – making therefore the article self-contained. Though probably they formally achieve this goal, the reviewer finds this part of exposition somewhat cumbersome (or, put it another way, “physics-inclined”), both in notations (big amount of tensor-calculus-like sub- and super-scripts) and accuracy (for example, one may guess that the ground field is of characteristic zero or even \(\mathbb C\) or \(\mathbb R\), though it is never stated explicitly).
Probably the most interesting (in the reviewer’s opinion) is the exposition of the results, due to the authors, about the higher-order Lie algebra structures related to classical simple Lie algebras and their cohomology.
Other topics include de Rham cohomology, BRST formalism, strong homotopy algebras and higher-order Poisson structures.
As each survey that is worth its name, it concludes with a large bibliography.