Algorithmic computations of Lie algebras cohomologies

Šilhan, Josef. "Algorithmic computations of Lie algebras cohomologies." Proceedings of the 22nd Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2003. [191]-197. <http://eudml.org/doc/221720>.

@inProceedings{Šilhan2003,
abstract = {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).},
author = {Šilhan, Josef},
booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
keywords = {Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[191]-197},
publisher = {Circolo Matematico di Palermo},
title = {Algorithmic computations of Lie algebras cohomologies},
url = {http://eudml.org/doc/221720},
year = {2003},
}

TY - CLSWK
AU - Šilhan, Josef
TI - Algorithmic computations of Lie algebras cohomologies
T2 - Proceedings of the 22nd Winter School "Geometry and Physics"
PY - 2003
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [191]
EP - 197
AB - 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).
KW - Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221720
ER -