On ideals in group algebras: An uncertainty principle and the Schur product

Hecke Algebras and Schur Algebras of the Symmetric Group

These notes give a fully self{contained introduction to the (modular) representation theory of the Iwahori{Hecke algebras and the q{Schur algebras of the symmetric groups. The central aim of this work is to give a concise, but complete, and an elegant, yet quick, treatment of the classiication of the simple modules and of the blocks of these two important classes of algebras. Our approach is co...

On the Separating Ideals of Some Vector-valued Group Algebras

‘on Schur Algebras and Related Algebras Vi: Some Remarks on Rational and Classical Schur Algebras’

In a recent paper, Dipper and Doty, [2], introduced certain finite dimensional algebras, associated with the natural module of the general linear group and its dual, which they call rational Schur algebras. We give a proof, via tilting modules, that these algebra are in fact generalized Schur algebras. Using the same technique we show that certain finite dimensional algebras with classical grou...

Ultra and Involution Ideals in $BCK$-algebras

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

On products of T-ideals in free algebras and free group algebras

Let F be a field and A a free associative F -algebra or a group algebra of a free group with an infinite set X of generators. We find a necessary and sufficient condition for the inclusion I ′ ⊆ I , where I = I1 . . . Ik and I ′ = I ′ 1 . . . I ′ l are any products of T -ideals in A. A canonical reformulation in terms of products of group representation varieties answers a question posed in 198...