Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

There is another type of homology theory for Lie algebras : the Leibniz homology HL,(I~), defined as the homology of a complex (T g, d) where T ~ is the tensor module over g and the differential is a lifting of the preceding differential. In fact this theory is defined for a larger class of algebras : the Leibniz algebras (see 1 below). The aim of this paper is to compute HL.(I~ @gl) in terms o...

We describe a minimal unstable module presentation over the Steenrod algebra for the odd-primary cohomology of infinitedimensional complex projective space and apply it to obtain a minimal algebra presentation for the cohomology of the classifying space of the infinite unitary group. We also show that there is a unique Steenrod module structure on any unstable cyclic module that has dimension o...

Let H(S) be the Hardy space on the unit sphere S in C, n ≥ 2. Then H(S) is a natural Hilbert module over the ball algebra A(B). Let Mz1 , ..., Mzn be the module operators corresponding to the multiplication by the coordinated functions. Each submodule M ⊂ H(S) gives rise to the module operators ZM,j = Mzj |M, j = 1, ..., n, on M. In this paper we establish the following commonly believed, but n...

Arithmetic of K3 surfaces defined over finite fields are investigated. In particular, we show that any K3 surface X of finite height over a finite field k of characteristic p ≥ 5 has a quasi-canonical lifting Z to characteristic 0, and that for any such Z, the endormorphism algebra of the transcendental cycles V (Z), as a Hodge module, is a CM field over Q. We illustrate by examples how to dete...

A recent result of ours [GM] shows that all Hopf algebra liftings of a given diagram in the sense of Andruskiewitsch and Schneider are cocycle deformations of each other. Here we develop a ‘non-abelian’ cohomology theory, which gives a method for an explicit description of cocycles relevant to the lifting process. 0. Introduction The Nichols algebra B(V ) of a crossed kG-module V is a connected...

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors in the algebra A C of the cylinder, and an isomorphism between the free module A C and its direct sum A C ⊕ F C with the Fock module on the cylinder. We cons...

Let L = ? j 1 m X 2 be a Hörmander sum of squares vector fields in space R n , where any is homogeneous degree with respect to family non-isotropic dilations space. In this paper we prove global estimates and regularity properties for the -Sobolev spaces W k p ( ) { … } . our approach, combine local results general sums squares, homogeneity property 's, plus lifting technique fields.

purpose: low back pain is one of the most common musculoskeletal disorders, and lifting is one of its risk factors. the activities of lumbar muscles as the main muscles involved in lifting are important with regard to identification of the allowable limits and the injury mechanisms as well as the motor control aspects. this study aimed to investigate the effects of the lifting speed on the lumb...