- Referenced in 142 articles
- theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their ... directly with elements of the Lie groups and algebras themselves; it rather computes with weights ... characters and similar objects. Some specialities of LiE are: tensor product decompositions, branching to subgroups ... about Lie group theoretical concepts and about currently valid definitions and values. Computer algebra system...
- Referenced in 38 articles
- LieART - A Mathematica Application for Lie Algebras and Representation Theory. We present the Mathematica application ... LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie Algebras and representation ... handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight...
- Referenced in 195 articles
- tables of groups of Lie type, Coxeter groups, Iwahori-Hecke algebras and other related structures...
- Referenced in 23 articles
- PASCAL programs for identification of Lie algebras. III: Levi decomposition and canonical basis. These ... PASCAL for the identification of a Lie algebra L (given by its structure constants ... LEVI to present a given Lie algebra with a standardized basis and gives possibilities ... comparison with other Lie algebras. Examples of Lie algebras with canonical bases...
- Referenced in 30 articles
- package which, together with Sage, performs Lie algebra computations using string junctions. py-junctions: This ... studying string junctions and their associated Lie algebraic structure. It is authored by J. Halverson...
- Referenced in 19 articles
- Mathematica package for calculations in Lie algebras and superalgebras. SuperLie is a Mathematica-based package ... scientific and computational problems related to Lie algebras and Lie superalgebras, their q-deformations included ... mathematician (vector spaces and superspaces, algebras and modules over these algebras) in a way (hopefully ... vacuum vectors (highest and lowest), compute Lie (super)algebra homology and cohomology; calculate the Shapovalov...
- Referenced in 27 articles
- topological spaces are conveniently expressed by algebraic invariants of the space. This paper focuses ... example with calculations of Lie algebra homology...
- Referenced in 18 articles
- package LAGUNA: Lie AlGebras and UNits of group Algebras. The LAGUNA package replaces ... group and for investigation of Lie algebra associated with group algebras and other associative algebras...
- Referenced in 25 articles
- also some support for combinatorial Lie algebras, operads, (affine) Weyl groups, crystals, Schubert polynomials...
- Referenced in 16 articles
- differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces ... recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development...
- Referenced in 20 articles
- characters of irreducible representations of semisimple Lie algebras, including functions for computing weight multiplicities, tensor...
- Referenced in 10 articles
- package Sophus: Computing in nilpotent Lie algebras. Sophusis a GAP4 package to compute with nilpotent ... Lie algebras over finite prime fields. In particular, the package can be used to compute ... test isomorphism between two nilpotent Lie algebras. The author of the package used ... construct all Lie algebras of dimension at most 9 over...
- Referenced in 9 articles
- PASCAL programs for identification of Lie algebras. II: SPLIT - a program to decompose parameter-free ... parameter-dependent Lie algebras into direct sums. The program SPLIT (based on PASCAL) contains ... determines a decomposition of a given Lie algebra L into the direct sum of smaller ... Lie algebras, if such a decomposition exists. The decomposition algorithm is basing on the fact...
- Referenced in 8 articles
- Lie algebraic computation In this paper the authors describe some basic algorithms for the structure ... determination of Lie algebras. They are implemented in a general library of Lie algebra algorithms ... called ELIAS (for Eindhoven LIe Algebra System) which is built into the computer algebra package ... aims at an interactive book on Lie algebras [A. M. Cohen and L. Meertens...
- Referenced in 15 articles
- aspects of the theory of simple Lie algebras (in characteristic...
- Referenced in 7 articles
- Computing with real Lie algebras: real forms, Cartan decompositions, and Cartan subalgebras. We describe algorithms ... various tasks related to real simple Lie algebras. These algorithms form the basis ... efficiently construct real simple Lie algebras up to isomorphism. Second, we consider a real semisimple ... Lie algebra 𝔤. We provide an algorithm for constructing a maximally (non-)compact Cartan subalgebra...
- Referenced in 56 articles
- length of the equations for large bilinear algebraic systems is presented. The integrable polynomial vector ... equations, quadratic Hamiltonians with an e(3) Lie-Poisson structure and nonlocal 2+1-dimensional ... studied. An overview of the computer algebra program CRACK used in this paper is given...
- Referenced in 10 articles
- with g a simple Lie algebra, l a nonnegative integer called the level...
- Referenced in 115 articles
- Macsyma program for the calculation of Lie point symmetries of large systems of differential equations ... works only under Macsyma, the commercial computer algebra system. The 1991 version of symmgrp.max (with...
- Referenced in 6 articles
- classification problems in geometry and algebra. The first problem we are currently working on deals ... classification of low dimensional Lie algebras. The software which supports our work on these ... programs for computations in differential geometry, Lie algebras and the variational calculus on jet spaces...