.. _SectLieQUAE:

.. _descriptions:

Universal Enveloping Algebras  and Quantum Groups
=================================================

Given a semisimple Lie algebra over a field of characteristic zero, we can
construct an integral basis for its universal enveloping algebra. Functionality
for computing in these algebras is described in
Section :ref:`SectUnivEA`. Moreover, we provide functionality for
computing in their quantised versions, which are called quantum groups. This is
described in Chapter :ref:`chap:quaGrps`.