On when small semiprime rings are slender

Various semiprime rings with less than 2^w elements are shown to be slender     

Towers of Corings

Abstract

The notion of a Frobenius coring is introduced, and it is shown that any such coring produces a Jones-like tower of Frobenius corings and Frobenius extensions. This establishes a one-to-one correspondence between Frobenius corings and extensions.     

The Canonical Basis for the Quantum Group of Type B2

We use the Ringel-Hall algebra approach to study the canonical basis elements for the quantum group of type B₂ which are characterized in Xi [12]. However, our approach simplifies several computations there.     

The K-Theory of Cuntz–Krieger Algebras for Infinite Matrices

We compute the K-theory groups of the Cuntz–Krieger C^*-algebra O_A associated to an infinite matrix A of zeros and ones.     

Homological Algebra for Coalgebraic Modules and Mod p K-Theory of Infinite Loop Spaces

In this paper, we develop the theory of homological algebra for coalgebraic modules, and compute and p K-theory of infinite loop spaces associated to BP-module spectra.     

Quasigraded lie algebras,Kostant-Adler scheme,and integrable hierarchies

Using special anisotropic quasigraded Lie algebras, we obtain a number of new hierarchies of integrable nonlinear equations in partial derivatives admitting zero-curvature representations. Among them are an anisotropic deformation of the Heisenberg magnet hierarchy, a matrix and vector generalization of the Landau—Lifshitz hierarchies, new types of matrix and vector anisotropic chiral-field hierarchies, and other types of anisotropic hierarchies.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 329–345, February, 2005.     

Canonical Representations and Overgroups for Hyperboloids of One Sheet and Lobachevsky Spaces

We define canonical representations for the hyperboloid of one sheet and for the Lobachevsky space =G/K where G=SO₀(1,n–1), H=SO₀(1,n–2) and K=SO(n–1), as the restriction to G of representations associated with a cone of overgroups and for and respectively. We determine explicitly the interaction of Lie operators of with operators intertwining canonical representations and representations of G associated with a cone.Mathematics Subject Classifications (2000) 43A85, 22E46, 53D55.V. F. Molchanov: Supported by grants of the Netherlands Organization for Scientific Research (NWO): 047-008-009, the Russian Foundation for Basic Research (RFBR): 01-01-00100-a, the Minobr RF: E00-1.0-156, the NTP Univ. Rossii: ur04.01.037.     

Free and semi-inert cell attachments

Let be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex.

We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously-studied inert condition. Under these conditions we determine as an -module and as an -algebra, respectively. Under a further condition we show that is generated by Hurewicz images.

As an example we study an infinite family of spaces constructed using only semi-inert cell attachments.

     

Bialgebra Cyclic Homology with Coefficients

We show that one can extend the definition of Hopf cyclic homology with coefficients such that one can use bialgebras and a larger class of coefficient module/co-modules. With the help of this extension, we calculate the bialgebra cyclic homology of U_q() the quantum deformation of an arbitrary semi-simple Lie algebra and (N) the Hopf algebra of foliations of codimension N, with several coefficient modules.