Casimir invariants for quantized affine Lie algebras

Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.     

Foxby equivalence, complete modules, and torsion modules

Taking the idea from classical Foxby equivalence, we develop an equivalence theory for derived categories over differential graded algebras. Both classical Foxby equivalence and the Morita equivalence for complete modules and torsion modules developed by Dwyer and Greenlees arise as special cases.     

Differential rings and ore extensions: Brown-McCoy rings

We consider here a ringK, a derivationD ofK and the differential polynomial ringR=K[X;D]. The ringK is said to be a Brown-McCoy ring if the prime radical coincides with the Brown-McCoy radical in every homomorphic image ofK. AD-Brown-McCoy ring is defined in a similar way. We prove the following conditions are equivalent: (i)K is aD-Brown-McCoy ring; (ii)R is a Brown-McCoy ring and for every maximal idealM ofR,K/(MνK) is aD-simple ring with 1. In addition, we give some applications and examples on the study of the transfer of the property of being a Brown-McCoy ring betweenK andR. Further, we study the relation between the prime and theD-prime ideals of a differential intermediate extension of a liberal extension. This paper was supported by a fellowship awarded by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.     

Quantum homogeneous spaces,duality and quantum 2-spheres

For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podle is established.     

Special radicals of near-rings and Γ-near-rings

It was previously shown that every special radical classR of rings induces a special radical class R of -rings. Amongst the special radical classes of near-rings, there are some, called the -special radical classes, which induce, special radical classes of -near-rings by the same procedure as used in the ring case. The -special radicals of near-rings possess very strong hereditary properties. In particular, this leads to some new results for the equiprime andI ₃ radicals.     

Convexity theories 0. Foundations

For an arbitrary prenormed semiring, the closed unit ball functor from the category _R pnSmod ¹ ofR-prenormedR-semimodules with contractions to the category of sets has a left adjoint. For such a semiringR the notion of finitary convexity theory overR is introduced and the category C of -modules is defined. It is shown that the canonical functor _R pnSmod ¹ C has a left adjoint. In caseR is a banach semiring one has infinitary convexity theories, in addition to the finitary ones, and again the canonical functor _R bnSmod ¹ C has a left adjoint.Many more happy returns, Nico. Sixty is forever.     

A star-product approach to noncompact quantum groups

Using the duality and the topological theory of well-behaved Hopf algebras, we construct star-product models of noncompact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on allC functions, and they even exist for nonlinear (semi-simple) Lie groups.     

Groups with a maximality condition for some non-normal subgroups

We describe (generalized) soluble-by-finite groups in which the set of non-normal subgroups which are not finitely generated satisfies the maximal condition.     

Complement preserving operators

An operatorTVV on a real inner product space is called complement preserving if, wheneverU is aT-invariant subspace ofV the orthogonal complementU is alsoT-invariant. In this note we obtain some results on such operators.     

On a certain identity satisfied by a derivation and an arbitrary additive mapping II

Summary The structure of prime ringsR and nonzero derivationsd onR, satisfyingd(x)f(x) = 0 for allx R, is described,f being a nonzero additive mapping ofR. Supported in part by a grant from the Ministry of Science of Slovenia.