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

Impact of Medicare denials on noninvasive vascular diagnostic testing

AbstractPurpose: The purpose of this study was to evaluate the impact of Medicare coverage limitations and claim denials on noninvasive vascular diagnostic testing. Methods: All Medicare claims for noninvasive vascular diagnostic studies from January 1, 1999, to December 31, 1999, were identified from the hospital billing database according to Current Procedural Terminology codes for carotid artery duplex ultrasound scan, venous duplex ultrasound scan, and lower-extremity arterial Doppler scan. Reasons for Medicare denial of payment for these tests were reviewed and a cost analysis was performed. Results: During the 1-year period, there were 1096 noninvasive vascular diagnostic studies performed on Medicare patients. Of these 1096 tests, 176 (16.1%) were denied by Medicare (19.6% of 408 carotid duplex ultrasound scans, 16.8% of 345 venous duplex ultrasound scans, and 11.1% of 343 lower-extremity arterial Doppler scans). Of the noninvasive vascular tests denied by Medicare, an abnormal result was present in 72.5% of carotid duplex ultrasound scans, 32.8% of venous duplex ultrasound scans, and 78.9% of lower-extremity arterial Doppler scans. Overall, 88.1% of all initially denied claims (N = 176) were ultimately reimbursed by Medicare after resubmission, including 77.1% of the 118 claims denied based on compliance rules for “medical necessity.” Conclusion: Because of coverage limitations, Medicare denials of noninvasive vascular diagnostic tests can lead to potential uncompensated physician and hospital technical fees if denied claims are unrecognized. Vascular laboratories performing these tests need to review compliance with Medicare guidelines. Improvements may need to be made at both the provider and Medicare carrier levels in obtaining reimbursement for appropriately ordered noninvasive vascular diagnostic studies. (J Vasc Surg 2001;34:846-53.

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

Cardiac Troponin Assessment Following Atrial Fibrillation Ablation: Implications for Chest Pain Evaluation

Background: The range of elevation of troponin I (tI) that is within expected limits from left atrial radiofrequency ablation for atrial fibrillation (AF) is not well described, though such information may be of clinical value. Objectives: Identify the expected range of tI values post-atrial fibrillation (AF) ablation. Methods: 31 patients undergoing AF ablation had a single tI level drawn the day following the procedure. Clinical variables were also collected, such as ablation type and radiofrequency (RF) time. Results: Paroxysmal AF was present in 23 patients, and 8 had chronic AF. The average RF time was 2627.8 ± 737.5 seconds. The mean RF power was 61.7 ± 4.3W (range 55-70W). The mean RF temperature limit was 53.6 ± 2.0°C (range 50-55°C). There was no clinical or electrocardiographic evidence of coronary ischemia in this population. The mean tI the following day was 3.21 ± 1.5 (range 1.48-8.41). There was no correlation between RF time, ablation type, ablation catheter size, and ablation temperature or ablation power and tI levels. Conclusions: Troponin I elevation post-ablation was ubiquitous. Knowledge of expected post-ablation tI levels may be helpful in the evaluation of post-procedure chest pain

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

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

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

High-performance diamond-based single-photon sources for quantum communication

Quantum communication places stringent requirements on single-photon sources. Here we report a theoretical study of the cavity Purcell enhancement of two diamond point defects, the nickel-nitrogen (NE8) and silicon-vacancy (SiV) centers, for high-performance, near on-demand single-photon generation. By coupling the centers strongly to high-finesse optical photonic-bandgap cavities with modest quality factor Q = O(10^4) and small mode volume V = O(\lambda^3), these system can deliver picosecond single-photon pulses at their zero-phonon lines with probabilities of 0.954 (NE8) and 0.812 (SiV) under a realistic optical excitation scheme. The undesirable blinking effect due to transitions via metastable states can also be suppressed with O(10^{-4}) blinking probability. We analyze the application of these enhanced centers, including the previously-studied cavity-enhanced nitrogen-vacancy (NV) center, to long-distance BB84 quantum key distribution (QKD) in fiber-based, open-air terrestrial and satellite-ground setups. In this comparative study, we show that they can deliver performance comparable with decoy state implementation with weak coherent sources, and are most suitable for open-air communication.Comment: 12 pages, 6 figures, 3 tables, revisions to excitation parameter