irreducible module

irreducible module

[‚ir·i¦dü·sə·bəl ′mäj·əl]
(mathematics)
A module whose only submodules are the module itself and the module that consists of the element 0.
References in periodicals archive ?
k]-module [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which decomposes into irreducibles as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where the multiplicity of each irreducible module is exactly one.
k] denote the irreducible module indexed by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Let denote the irreducible module labeled by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
It follows that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is irreducible and that signed conjugation produces a complete set of irreducible modules for the planar algebras.
1) In a model representation, isotypic components are irreducible components, so projection operators map directly onto irreducible modules without being mixed up among multiple isomorphic copies of the same module.
When Bk(x) is semisimple, its irreducible modules are indexed by partitions in the set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
lambda]] denotes the irreducible module corresponding to [lambda] then [D.
Imprimitive Irreducible Modules for Finite Quasisimple Groups
The contributors discuss known results and methods for determining root multiplicities for hyperbolic Kac-Moody algebras, results in Leibniz algebras which are analogs of corresponding results in Lie algebras, Weyl modules for quantum and hyper loop algebras, and Koszul properties of standard and irreducible modules.