Thin Coverings of Modules
نویسنده
چکیده
Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian groups. The classification uses the representation theory of cyclotomic quantum tori. We close with an application to representations of multiloop Lie algebras.
منابع مشابه
ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS
Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...
متن کاملImproved Coverings of a Square with Six and Eight Equal Circles
In a recent article 19], Tarnai and GG aspp ar used computer simulations to nd thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius.
متن کاملCoverings and crossed modules of topological groups with operations
It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G . In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We ...
متن کاملQuasigroups, right quasigroups and category coverings
The category of modules over a fixed quasigroup in the category of all quasigroups is equivalent to the category of representations of the fundamental groupoid of the Cayley diagram of the quasigroup in the category of abelian groups. The corresponding equivalent category of coverings, and the generalization to the right quasigroup case, are also described.
متن کاملJa n 20 04 The influence of complex material coverings on the bandwidth of antennas
The influence of material coverings on the antenna bandwidth is investigated for antennas formed by thin electric or magnetic line sources. It is shown that uniform thin layers of arbitrary passive materials (including Veselago, left-handed, or double-negative materials) cannot help to overcome the bandwidth limitations imposed by the amount of energy stored in the antenna reactive field. Alter...
متن کامل