Author:
Bahturin Yuri,Kochetov Mikhail,Shihadeh Abdallah
Abstract
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 sl2(C), we consider specific gradings on simple modules of arbitrary dimension.
Publisher
Universidad Nacional de Colombia
Reference22 articles.
1. B. Allison, S. Berman, J. Faulkner, and A. Pianzola, Realization of graded-simple algebras as loop algebras, Forum Math. 20 (2008), 395-432.
2. D. Arnal and G. Pinczon, On algebraically irreducible representations of the Lie algebra sl(2), J. Math. Phys. 15 (1974), 350-359.
3. Y. Bahturin, S. Sehgal, and M. Zaicev, Group gradings on associative algebras, J. Algebra 241 (2001), 667-698.
4. V. Bavula, Classification of simple sl(2)-modules and the finite dimensionality of the module of extensions of simple sl(2)-modules, (Russian), Ukrain. Mat. Zh. 42 (1990), 1174-1180, translation in Ukrainian Math. J. 42 (1990), 1044-1049 (1991).
5. V. Bavula, Generalized Weyl algebras and their representations, (Russian), Algebra i Analiz 4 (1992), 75-97, translation in St. Petersburg Math. J. 4 (1993), 71-92.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献