https://github.com/laughedelic/m-cohomology

Basic abstractions and methods for computations in terms of group algebra Z[G] and automatic construction of cocycle translations for computation of cup-product.
https://github.com/laughedelic/m-cohomology

algebra category-theory cohomology haskell mathematics maths thesis

Last synced: 4 days ago
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Basic abstractions and methods for computations in terms of group algebra Z[G] and automatic construction of cocycle translations for computation of cup-product.

• Host: GitHub
• URL: https://github.com/laughedelic/m-cohomology
• Owner: laughedelic
• License: lgpl-3.0
• Created: 2012-06-09T23:41:54.000Z (over 12 years ago)
• Default Branch: master
• Last Pushed: 2015-12-08T00:48:12.000Z (almost 9 years ago)
• Last Synced: 2024-10-17T02:39:36.257Z (20 days ago)
• Topics: algebra, category-theory, cohomology, haskell, mathematics, maths, thesis
• Language: Haskell
• Homepage:
• Size: 10.7 KB
• Stars: 6
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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## Description

This is a part of my diploma thesis on computaion of integral cohomology algebra of modular 2-groups. This Haskell library offers some basic abstractions and methods for computations in terms of the group algebra `Z[G]` and automatic construction of cocycle traslations for computation of the cup-product.

### References

For more details about the work, see the following publication:

- [Hochschild cohomology ring of the modular group](http://dx.doi.org/10.1090/S1061-0022-2014-01328-3)  

  _Abstract:_ A description in terms of generators and relations is given for the cohomology ring and the Hochschild cohomology ring of the group algebra for the even modular group over the ring of integers. The free resolution of the trivial module described by Wall is used for that. Moreover, the bimodule resolution of the group algebra in question is described.

- This code uses the [sparse-lin-alg](https://github.com/laughedelic/sparse-lin-alg) Haskell library

### Disclaimer

The code is present here just for the sake of sharing the approach that I used in my research.