Year: 2016
Type: preprint
Abstract: Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be isomorphic to each other. Under some restrictions, these loop modules are completely reducible (as ungraded modules), and some of their invariants --- inertia group, graded Brauer invariant and Schur index --- which were previously defined for simple modules over graded finite-dimensional semisimple Lie algebras over an algebraically closed field of characteristic zero, are now considered in a more general and natural setting.
Source: arXiv (Cornell University)
Authors: Elduque, Alberto, Kochetov, Mikhail
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2543258469, G346970137
OpenAlex ID: W4300828503