# lie: Library for the representation theory of complex semisimple Lie groups and algebras¶

## Description¶

LiE is the name of a software package that enables mathematicians and physicists to perform computations of a Lie group theoretic nature. It focuses on the representation theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their Weyl groups and root systems.

LiE does not compute directly with elements of the Lie groups and algebras themselves; it rather computes with weights, roots, characters and similar objects. Some specialities of LiE are: tensor product decompositions, branching to subgroups, Weyl group orbits, reduced elements in Weyl groups, distinguished coset representatives and much more. These operations have been compiled into the program which results in fast execution: typically one or two orders of magnitude faster than similar programs written in a general purpose program.

The LiE programming language makes it possible to customise and extend the package with more mathematical functions. A user manual is provided containing many examples.

LiE establishes an interactive environment from which commands can be given that involve basic programming primitives and powerful built-in functions. These commands are read by an interpreter built into the package and passed to the core of the system. This core consists of programs representing some 100 mathematical functions. The interpreter offers on-line facilities which explain operations and functions, and which give background information about Lie group theoretical concepts and about currently valid definitions and values.

GNU Lesser General Public License (LGPL), version unspecified

## Dependencies¶

• ncurses

• bison (not included in this package or in Sage!)

experimental

## Version Information¶

package-version.txt:

2.2.2


## Equivalent System Packages¶

macports: install the following packages: lie See https://repology.org/project/lie/versions

However, these system packages will not be used for building Sage because spkg-configure.m4 has not been written for this package; see https://trac.sagemath.org/ticket/27330