We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.

let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.

Let H be a Hopf algebra over a field k and A a right coideal subalgebra of H , that is, A is a subalgebra satisfying ∆(A) ⊂ A⊗H where ∆ is the comultiplication in H . In case when H is finitely generated commutative, the right coideal subalgebras are intimately related to the homogeneous spaces for the corresponding group scheme. The purpose of this paper is to extend the class of pairsA,H for ...

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

Rational approaches have been extensively used to investigate the role of active site residues in cytochrome P450 (CYP) functions. However, recent studies using random mutagenesis suggest an important role for non-active site residues in CYP functions. Meta-analysis of the random mutants showed that 75% of the functionally important non-active site residues are present in 20% of the entire prot...