A note on short and long exact sequences in the BBG construction of complexes from complexes
Provides a theoretical framework for understanding cohomology in BGG sequences, relevant to researchers in numerical analysis of PDEs.
The paper shows how cohomology of certain BGG sequences used in numerical PDE analysis can be derived via long exact sequences, and extends this to non-injective/surjective cases using short exact sequences of complexes.
We first show how the cohomology of some Bernstein-Gelfand-Gelfand (BGG) sequences that are important for the numerical analysis of partial differential equations, can be obtained through the construction of a long exact sequence connecting cohomology groups. Then we explain the extension of this result to the non-injective/surjective case through the systematic use of short exact sequences of complexes and their associated long exact sequences of cohomology groups. Finally an interpretation in terms of spectral sequences is given.