Group algebras and enveloping algebras with nonmatrix and semigroup identities

Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity not satisfied by the algebra of all 2-by-2 matrices over K. Then we examine those R for which I satisfies a semigroup identity (that is, a polynomial identity which can be written as the difference of two monomials).Comment: 11 pages. Written in LaTeX2

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

Simple algebras of Weyl type

Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl type on the same vector space $A[D]=A\otimes F[D]$ are defined. It is proved that $A[D]$, as a Lie algebra (modular its center) or as an associative algebra, is simple if and only if $A$ is $D$-simple and $A[D]$ acts faithfully on $A$. Thus a lot of simple algebras are obtained.Comment: 9 pages, Late

Comparison of axillofemoral and aortofemoral bypass for aortoiliac occlusive disease

AbstractPurpose: A comparison of aortofemoral bypass grafting (AOFBG) and axillofemoral bypass grafting (AXFBG) for occlusive disease performed by the same surgeons during a defined interval forms the basis for this report.Methods: Data regarding all patients who underwent AOFBG or AXFBG for lower-extremity ischemia caused by aortoiliac occlusive disease were prospectively entered into a computerized vascular registry. The decision to perform AOFBG rather than AXFBG was based on assessment of surgical risk and the surgeon's preference. This report describes results for surgical morbidity, mortality, patency, limb salvage, and patient survival for procedures performed from January 1988 through December 1993.Results: We performed 108 AXFBGs and 139 AOFBGs. AXFBG patients were older (mean age, 68 years compared with 58 years for AOFBG, p < 0.001), more often had heart disease (84% compared with 38%, p < 0.001), and more often underwent surgery for limb-salvage indications (80% compared with 42%, p < 0.001). No significant differences were found in operative mortality (AXFBG, 3.4%; AOFBG, <1.0%, p = NS), but major postoperative complications occurred more frequently after AOFBG (AXFBG, 9.2%; AOFBG, 19.4%; p < 0.05). Follow-up ranged from 1 to 83 months (mean, 27 months). Five-year life-table primary patency, limb salvage, and survival rates were 74%, 89%, and 45% for AXFBG and 80%, 79%, and 72% for AOFBG, respectively. Although the patient survival rate was statistically lower with AXFBG, primary patency and limb salvage rates did not differ when compared with AOFBG.Conclusion: When reserved for high-risk patients with limited life expectancy, the patency and limb salvage results of AXFBG are equivalent to those of AOFBG. (J VASC SURG 1996;23:263-71.

The Ideal Intersection Property for Groupoid Graded Rings

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property

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

A Transcriptomic Signature of Mouse Liver Progenitor Cells

Liver progenitor cells (LPCs) can proliferate extensively, are able to differentiate into hepatocytes and cholangiocytes, and contribute to liver regeneration. The presence of LPCs, however, often accompanies liver disease and hepatocellular carcinoma (HCC), indicating that they may be a cancer stem cell. Understanding LPC biology and establishing a sensitive, rapid, and reliable method to detect their presence in the liver will assist diagnosis and facilitate monitoring of treatment outcomes in patients with liver pathologies. A transcriptomic meta-analysis of over 400 microarrays was undertaken to compare LPC lines against datasets of muscle and embryonic stem cell lines, embryonic and developed liver (DL), and HCC. Three gene clusters distinguishing LPCs from other liver cell types were identified. Pathways overrepresented in these clusters denote the proliferative nature of LPCs and their association with HCC. Our analysis also revealed 26 novel markers, LPC markers, including Mcm2 and Ltbp3, and eight known LPC markers, including M2pk and Ncam. These markers specified the presence of LPCs in pathological liver tissue by qPCR and correlated with LPC abundance determined using immunohistochemistry. These results showcase the value of global transcript profiling to identify pathways and markers that may be used to detect LPCs in injured or diseased liver

Antimicrobial and antioxidant screening of curcumin and pyrocatechol in the prevention of biodiesel degradation: oxidative stability

Owing to its hygroscopicity biodiesel may accumulate water during storage, which becomes favorable to the growth of microorganisms. In order to control microbial contamination, use of various chemical biocides has been studied. However, the addition of a natural substance simultaneously with antioxidant and microbial growth inhibition could prove advantageous in the prevention of biodiesel oxidation and microbial contamination. Curcumin and pyrocatechol are antioxidant agents, which also exhibit microbial growth inhibition abilities. This research effort aimed at evaluating the addition of curcumin and pyrocatechol to biodiesel produced from various vegetable sources (waste frying oil, soybean oil, cottonseed oil, sesame oil, macaúba almond oil and microalgae oil). The combined addition of 1% (w/w) water and curcumin (viz. 0.2% (w/w) for biodiesel from spent frying oil, 0.5% (w/w) for biodiesel from soybean oil, 0.1% (w/w) for biodiesel from cotton seed oil, 0.5% (w/w) for biodiesel from sesame seed oil, 0.2% (w/w) for biodiesel from macaúba almond oil, and 0.2% (w/w) for biodiesel from microalgae oil) were those processing variables that promoted the best fungistatic and antioxidant effects, allowing maintenance of an unfavorable environment for microbial growth in biodiesel inoculated with the ubiquitous filamentous mold Paecilomyces variotii Bainier.Project funding by CNPq (National Council for Scientific and Technological Development - Brazil) (CNPq Ref. No. 404808/ 2013-1, Project ‘Studies on Biodiesel: Development of analytical methods for the characterization and quality control, and research of new natural additives to improve the quality of this biofuel’), is hereby gratefully acknowledged. This work received support from CNPq, National Council for Scientific and Technological Development Brazil, in the form of Research Productivity (PQ) fellowships granted to Victor M. Balcão (Ref. No. 306113/2014-7) and Marco V. Chaud (Ref. No. 309598/2014-1). The authors have no conflicts of interest whatsoever to declare

A Comparison of Atrial Fibrillation Monitoring Strategies After Cryptogenic Stroke (from the Cryptogenic Stroke and Underlying AF Trial)

Ischemic stroke cause remains undetermined in 30% of cases, leading to a diagnosis of cryptogenic stroke. Paroxysmal atrial fibrillation (AF) is a major cause of ischemic stroke but may go undetected with short periods of ECG monitoring. The Cryptogenic Stroke and Underlying Atrial Fibrillation trial (CRYSTAL AF) demonstrated that long-term electrocardiographic monitoring with insertable cardiac monitors (ICM) is superior to conventional follow-up in detecting AF in the population with cryptogenic stroke. We evaluated the sensitivity and negative predictive value (NPV) of various external monitoring techniques within a cryptogenic stroke cohort. Simulated intermittent monitoring strategies were compared to continuous rhythm monitoring in 168 ICM patients of the CRYSTAL AF trial. Short-term monitoring included a single 24-hour, 48-hour, and 7-day Holter and 21-day and 30-day event recorders. Periodic monitoring consisted of quarterly monitoring through 24-hour, 48-hour, and 7-day Holters and monthly 24-hour Holters. For a single monitoring period, the sensitivity for AF diagnosis was lowest with a 24-hour Holter (1.3%) and highest with a 30-day event recorder (22.8%). The NPV ranged from 82.3% to 85.6% for all single external monitoring strategies. Quarterly monitoring with 24-hour Holters had a sensitivity of 3.1%, whereas quarterly 7-day monitors increased the sensitivity to 20.8%. The NPVs for repetitive periodic monitoring strategies were similar at 82.6% to 85.3%. Long-term continuous monitoring was superior in detecting AF compared to all intermittent monitoring strategies evaluated (p <0.001). Long-term continuous electrocardiographic monitoring with ICMs is significantly more effective than any of the simulated intermittent monitoring strategies for identifying AF in patients with previous cryptogenic stroke