Reversible skew laurent polynomial rings and deformations of poisson automorphisms

A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1). We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field F. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in F-3 and the ring of invariants S-theta of the reversing automorphism is a deformation of B and is a factor of a deformation of F[x(1), x(2), x(3)] for a Poisson bracket determined by the appropriate surface

Irreducible actions and compressible modules

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a critically compressible left $B$-module, then the dimension of its self-injective hull $A$ over the ring of fractions of $A^B$ is bounded by the uniform dimension of $A$ and the number of linear operators generating $B$. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions

Nilpotent maximal subgroups of GLn(D)

AbstractIn [S. Akbari, J. Algebra 217 (1999) 422–433] it has been conjectured that if D is a noncommutative division ring, then D∗ contains no nilpotent maximal subgroup. In connection with this conjecture we show that if GLn(D) contains a nilpotent maximal subgroup, say M, then M is abelian, provided D is infinite. This extends one of the main results appeared in [S. Akbari, J. Algebra 259 (2003) 201–225, Theorem 4]

Del Pezzo surfaces of degree 1 and jacobians

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.Comment: 24 page

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Space Station and Space Cabin Testing

For Earth Orbiting Space Stations neither expandable, extensible, nor converted propellant tanks appear as suitable for manned operations as a specially designed cabin regardless of the mission to be performed. While an interesting possibility, use of converted propellant tanks offer little advantage when viewed in the light of the overall space station system problem. During the past two years studies have been conducted in some depth of the cabins associated with space station systems suitable for launch by Titan III C, Saturn IB, and Saturn 5 boosters. These studies have considered various crew complements, supporting ferries f and the effects of rotation for the generation of artificial G . Considering the requirements for integrating power supplies, thermal control* life support, attitude control, orbit propulsion, specific mission equipment, rendezvous, docking, communications, navigation, and crew creature comforts, the development of an efficient usable cabin becomes a task of significant proportions. Applying the constraints of removable and storable equipment to the fixed sizes and shapes of booster tankage makes the problem more difficult, the results less than optimum, and the increased cost substantial

How often should we monitor for reliable detection of atrial fibrillation recurrence? Efficiency considerations and implications for study design

OBJECTIVE: Although atrial fibrillation (AF) recurrence is unpredictable in terms of onset and duration, current intermittent rhythm monitoring (IRM) diagnostic modalities are short-termed and discontinuous. The aim of the present study was to investigate the necessary IRM frequency required to reliably detect recurrence of various AF recurrence patterns. METHODS: The rhythm histories of 647 patients (mean AF burden: 12±22% of monitored time; 687 patient-years) with implantable continuous monitoring devices were reconstructed and analyzed. With the use of computationally intensive simulation, we evaluated the necessary IRM frequency to reliably detect AF recurrence of various AF phenotypes using IRM of various durations. RESULTS: The IRM frequency required for reliable AF detection depends on the amount and temporal aggregation of the AF recurrence (p<0.0001) as well as the duration of the IRM (p<0.001). Reliable detection (>95% sensitivity) of AF recurrence required higher IRM frequencies (>12 24-hour; >6 7-day; >4 14-day; >3 30-day IRM per year; p<0.0001) than currently recommended. Lower IRM frequencies will under-detect AF recurrence and introduce significant bias in the evaluation of therapeutic interventions. More frequent but of shorter duration, IRMs (24-hour) are significantly more time effective (sensitivity per monitored time) than a fewer number of longer IRM durations (p<0.0001). CONCLUSIONS: Reliable AF recurrence detection requires higher IRM frequencies than currently recommended. Current IRM frequency recommendations will fail to diagnose a significant proportion of patients. Shorter duration but more frequent IRM strategies are significantly more efficient than longer IRM durations. CLINICAL TRIAL REGISTRATION URL: Unique identifier: NCT00806689

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy