We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for coactions of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras, and some quantum groups.

This is the second part of the article [3]. In the first paper we developed a cyclic homology theory for B–module coalgebras with coefficients in stable B–module/comodules where B was just a bialgebra. The construction we gave for the cyclic homology theory for B–module coalgebras used mainly the coalgebra structure on B. In the first part of this paper, we present the dual picture. Namely, a c...

Cyclic cohomology of Hopf algebras admitting a modular pair was first defined in [2] and further developed in [3] and [4] in the context of transverse geometry. Their results are followed by several papers computing Hopf cyclic (co)homology of certain Hopf algebras such as [15], [5] and [13]. In a series of papers [1], [10], [11], and [6] the authors developed a theory of cyclic (co)homology wh...

For positive integers n and l, we study the cyclic U(gl n )-module generated by the l-th power of the α-determinant det(X). This cyclic module is isomorphic to the n-th tensor space (Sym(C)) of the symmetric l-th tensor space of C for all but finite exceptional values of α. If α is exceptional, then the cyclic module is equivalent to a proper submodule of (Sym(C)), i.e. the multiplicities of se...

The quantum α-determinant is defined as a parametric deformation of the quantum determinant. We investigate the cyclic Uq(sl2)-submodules of the quantum matrix algebra Aq(Mat2) generated by the powers of the quantum α-determinant. For such a cyclic module, there exists a collection of polynomials which describe the irreducible decomposition of it in the following manner: (i) each polynomial cor...

In this paper we characterize the radical of an arbitrary‎ ‎submodule $N$ of a finitely generated free module $F$ over a‎ ‎commutatitve ring $R$ with identity‎. ‎Also we study submodules of‎ ‎$F$ which satisfy the radical formula‎. ‎Finally we derive‎ ‎necessary and sufficient conditions for $R$ to be a‎ ‎Pr$ddot{mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $Rbigopl...

For a (co)monad Tl on a category M, an object X in M, and a functor Π : M → C, there is a (co)simplex Z := ΠTl ∗+1 X in C. The aim of this paper is to find criteria for para(co)cyclicity of Z. Our construction is built on a distributive law of Tl with a second (co)monad Tr on M, a natural transformation i : ΠTl → ΠTr , and a morphism w : TrX → TlX in M. The (symmetrical) relations i and w need ...