On Tensor Products of Simple Modules for Simple Groups

Simple Tensor Products

Let F be the category of finite dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product S1⊗· · ·⊗SN of simple objects of F is simple if and only if for any i < j, Si ⊗ Sj is simple.

On the Tensor Products of Modules for Dihedral 2-Groups

The only groups for which all indecomposable modules are ‘knowable’ are those with cyclic, dihedral, semidihedral, and quaternion Sylow p-subgroups. The structure of the Green ring for groups with cyclic and V4 Sylow p-subgroups are known, but no others have been determined. Of the remaining groups, the dihedral 2-groups have the simplest module category but yet the tensor products of any two i...

On Extensions of Simple Modules over Symmetric and Algebraic Groups

Tensor Products of Modules

The notion of a tensor product of topological groups and modules is important in theory of topological groups, algebraic number theory. The tensor product of compact zero-dimensional modules over a pseudocompact algebra was introduced in [B] and for the commutative case in [GD], [L]. The notion of a tensor product of abelian groups was introduced in [H]. The tensor product of modules over commu...

Infinite Products of Finite Simple Groups

We classify the sequences 〈Sn | n ∈ N〉 of finite simple nonabelian groups such that ∏ n Sn has uncountable cofinality.