From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package $LiE$ offers the data structures and corresponding procedures for computing with semisimple Lie algebras. Thus, using $LiE$ it has been easy to implement the (theoretical) algorithm.The web implementation of the resulting algorithm is available online at the following address www.math.muni.cz/$\sim$silhan/lac. (These pages compute moreover cohomologies of real semisimple Lie algebras. These cohomologies will be described elsewhere).

EUDML-ID : urn:eudml:doc:221720
Mots clés:

@article{701718,
     title = {Algorithmic computations of Lie algebras cohomologies},
     booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2003},
     pages = {[191]-197},
     mrnumber = {MR1982446},
     zbl = {1032.17037},
     url = {http://dml.mathdoc.fr/item/701718}
}

Šilhan, Josef. Algorithmic computations of Lie algebras cohomologies, dans Proceedings of the 22nd Winter School "Geometry and Physics", GDML_Books,  (2003), pp. [191]-197. http://gdmltest.u-ga.fr/item/701718/