Now choose a Borel subgroup B in G and a maximal torus T in B so that, if B is the opposite Borel subgroup, then B ∩ H and B ∩ H are a Borel subgroups in H and T ∩H is a maximal torus in H . We follow the convention that the roots of B are positive. If λ ∈ X(T ), then indGB(−λ) is the dual Weyl module ∇G(λ ) with highest weight λ = −w0λ and lowest weight −λ. Its dual is the Weyl module ∆G(λ). I...

We introduce the notion of support equivalence for (co)module algebras (over Hopf algebras), which generalizes in a natural way (weak) gradings. show that each class algebra structures on given A, there exists unique universal H together with an H-(co)module structure A such any other equivalent factors through action H. study and mentioned above group gradings, Hopf-Galois extensions, actions ...

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra ...

Factor H is a regulatory glycoprotein of the complement system. We expressed the three N-terminal complement control protein modules of human factor H (FH1-3) and confirmed FH1-3 to be the minimal unit with cofactor activity for C3b proteolysis by factor I. We reconstructed FH1-3 from NMR-derived structures of FH1-2 and FH2-3 revealing an approximately 105-A-long rod-like arrangement of the mod...

We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule coalgebra in R. Moreover, a B-module coalgebra C is a member of R if, and only if, DB is in R for every simple subcoalgebra D of C. The collection of B-cocleft co...

This study was conducted to determine the effect of Cu deficiency on acute-phase protein concentrations, superoxide dismutase activity, leukocyte numbers, and lymphocyte proliferation in heifers inoculated with live bovine herpesvirus-1 (BHV-1). Hereford × Angus heifers were allotted by weight and initial liver Cu concentrations into molybdenum (Mo)-supplemented (n = 6) or control (n = 6) group...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...