Tensor products of quantized tilting modules

Dimensions of Quantized Tilting Modules

We will follow the notations of [7]. Let (Y,X, . . . ) be a simply connected root datum of finite type. Let p be a prime number bigger than the Coxeter number h. Let ζ be a primitive p-th root of unity in C. Let U be the quantum group with divided powers associated to these data. Let T be the category of tilting modules over U , see e.g. [1]. Recall that any tilting module is a sum of indecompo...

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...

Tensor Ideals in the Category of Tilting Modules

Let g be a complex finite dimensional simple Lie algebra with the root datum (Y,X, . . . ), see [Lu2]. Let Wf denote the Weyl group, R denote the root system, R+ denote the set of positive roots. Let X+ denote the set of dominant integral weights. Let h denote the Coxeter number of g. Let us fix l ∈ N, l > h. We assume that l is odd (and not divisible by 3, if g is of type G2). Let W denote the...

V.Ostrik TENSOR IDEALS IN THE CATEGORY OF TILTING MODULES.

Fuzzy projective modules and tensor products in fuzzy module categories

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...