Abstract

BAHTURIN, Yuri; KOCHETOV, Mikhail  and  SHIHADEH, Abdallah. Graded modules over simple Lie algebras. Rev.colomb.mat. [online]. 2019, vol.53, suppl.1, pp.45-86.  Epub Mar 24, 2020. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v53nsupl.84006.

The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra l2(ℂ), we consider specific gradings on simple modules of arbitrary dimension.

Keywords : graded Lie algebras; graded modules; simple modules; universal enveloping algebra.

        · abstract in Spanish     · text in English     · English ( pdf )