Computation of hochschild cohomology via morse matching

Аннотация

It is well known that the first cohomology group of an algebra is related to its derivations, and the elements of the second one describe its null extensions. Some believe that, in the theory of groups or algebras, we just need the first and the second groups of (co)homology, but it was shown that the elements of the third cohomology group can be applied to describe the obstacles to the construction of extensions. Homological algebra also introduces important numerical invariants in the group theory, e.g., (co)homological dimension and Euler characteristic. So we can say that homological methods allow us to get important information about the structure of an algebra.