Installation and Usage

Installation

This project relies on Sagemath, for installation instructions see: install Sagemath. The most recent version of this package is developed with Sagemath 9.0, but more recent versions should also work.

After installing sage run the following command:

sage -pip install git+https://github.com/RikVoorhaar/bgg-cohomology.git

In MacOS and linux this should run just fine. When using Windows, make sure to run this command from the Sagemath Shell.

To open the .ipynb files in the computations and examples folders, you can either launch Sagemath Notebook or run the following in the command line:

sage -n

Usage

We strongly recommend reading the general tutorial to get started. If you are only interested in the BGG complex itself, then look at the maps in BGG complex tutorial. If you want to compute the BGG cohomology of a lie algebra module defined as a quotient, see the tutorial on using cokernels. Finally for an introduction on how to use the functionality related to computing the Hochschild cohomology of (partial) flag varieties / the center off the small quantum group, see the quantum center tutorial.

Furthermore, the notebooks and scripts in the computations folder can also serve as examples. These files were used to generate the results published our arXiv preprint as well as for a paper yet to be published by the same authors on the center of the small quantum group.