It is known that the Fundamental Theorem of Hopf modules can be used to characterize Hopf algebras: a bialgebra H over a field is a Hopf algebra (i.e. it is endowed with a so-called antipode) if and only if every Hopf module M over H can be decomposed in the form M coH ⊗ H , where M coH denotes the space of coinvariant elements in M . A partial extension of this equivalence to the case of quasi...

We show that group algebras kG of polycyclic-by-finite groups G, where k is a field, are catenary: If P = I0 I1 · · · Im = P ′ and P = J0 J2 · · · Jn = P ′ are both saturated chains of prime ideals of kG, then m = n.

A module MR is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and MR be a α-compatible module and T = R[[x;α]]. It is shown that M [[x]]T is right p.q.-Baer if and only if MR is right p.q.-Baer and the right annihilator of any countably-generated ...

We study the algebraic Gauss-Manin system and the algebraic Brieskorn module associated to a polynomial mapping with isolated singularities. Since the algebraic GaussManin system does not contain any information on the cohomology of singular fibers, we construct a non quasi-coherent sheaf which gives the cohomology of every fiber. Then we study the algebraic Brieskorn module by comparing it wit...

In investigating homotopy equivalences of smooth G-manifolds where G is a compact Lie group, Pétrie [3], [4], [5] makes use of proper G-maps of degree 1 from one G-module to another of the same complex dimension. The first nontrivial example of such a map, called a quasi-equivalence, was given by Pétrie [6] for two-dimensional S -modules. Necessary and sufficient conditions for the existence of...

Let G be a quasi simply reducible group, and let V be a representation of G over the complex numbers C. In this thesis, we introduce the twisted 6j-symbols over G which have their origin to Wigner’s 6j-symbols over the group SU(2) to study the structure constants of the subrepresentation semiring SG(End(V )), and we study the representation theory of a quasi simply reducible group G laying emph...

∇−good filtration dimensions of modules and of algebras are introduced by Parker for quasi-hereditary algebras. These concepts are now generalized to the setting of standardly stratified algebras. Let A be a standardly stratified algebra. The ∇-good filtration dimension of A is proved to be the projective dimension of the characteristic module of A. Several characterizations of ∇good filtration...

We construct quantum commutators on module-algebras of quasitriangular Hopf algebras. These are quantum-group covariant, and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy a generalized Jacobi identity, turning the modulealgebra into a quantum-Lie algebra. The purpose of this short communication is to present a quantum commutato...

Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X = C. Let D ⊂ X be a locally weakly quasi-homogeneous free divisor defined by a polynomial f . In this paper we prove that, locally, the annihilating ideal of 1/f over DX is generated by linear differential operators of order 1 (for k big enough). For this...