The Local Structure of Lie Bialgebroids

We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical $r$-matrices and matched pairs induced by Poisson group actionsComment: 13 page

Star formation associated with a large-scale infrared bubble

Using the data from the Galactic Ring Survey (GRS) and Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE), we performed a study for a large-scale infrared bubble with a size of about 16 pc at a distance of 2.0 kpc. We present the 12CO J=1-0, 13CO J=1-0 and C18O J=1-0 observations of HII region G53.54-0.01 (Sh2-82) obtained at the the Purple Mountain Observation (PMO) 13.7 m radio telescope to investigate the detailed distribution of associated molecular material. The large-scale infrared bubble shows a half-shell morphology at 8 um. H II regions G53.54-0.01, G53.64+0.24, and G54.09-0.06 are situated on the bubble. Comparing the radio recombination line velocities and associated 13CO J=1-0 components of the three H II regions, we found that the 8 um emission associated with H II region G53.54-0.01 should belong to the foreground emission, and only overlap with the large-scale infrared bubble in the line of sight. Three extended green objects (EGOs, the candidate massive young stellar objects), as well as three H II regions and two small-scale bubbles are found located in the G54.09-0.06 complex, indicating an active massive star-forming region. C18O J=1-0 emission presents four cloud clumps on the northeastern border of H II region G53.54-0.01. Via comparing the spectral profiles of 12CO J=1-0, 13CO J=1-0, and C18O J=1-0 peak at each clump, we found the collected gas in the three clumps, except for the clump coincided with a massive YSO (IRAS 19282+1814). Using the evolutive model of H II region, we derived that the age of H II region G53.54-0.01 is 1.5*10^6 yr. The significant enhancement of several Class I and Class II YSOs around G53.54-0.01 indicates the presence of some recently formed stars, which may be triggered by this H II region through the collect and collapse (CC) process.Comment: 9 pages, 6 figures, accepted for publication in A&

Manin Triples for Lie Bialgebroids

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except on certain subspaces. In this paper we systematize the properties of this bracket in the definition of a Courant algebroid. This structure on a vector bundle $E\rightarrow M$, consists of an antisymmetric bracket on the sections of $E$ whose ``Jacobi anomaly'' has an explicit expression in terms of a bundle map $E\rightarrow TM$ and a field of symmetric bilinear forms on $E$. When $M$ is a point, the definition reduces to that of a Lie algebra carrying an invariant nondegenerate symmetric bilinear form. For any Lie bialgebroid $(A,A^{*})$ over $M$ (a notion defined by Mackenzie and Xu), there is a natural Courant algebroid structure on $A\oplus A^{*}$ which is the Drinfel'd double of a Lie bialgebra when $M$ is a point. Conversely, if $A$ and $A^*$ are complementary isotropic subbundles of a Courant algebroid $E$, closed under the bracket (such a bundle, with dimension half that of $E$, is called a Dirac structure), there is a natural Lie bialgebroid structure on $(A,A^{*})$ whose double is isomorphic to $E$. The theory of Manin triples is thereby extended from Lie algebras to Lie algebroids. Our work gives a new approach to bihamiltonian structures and a new way of combining two Poisson structures to obtain a third one. We also take some tentative steps toward generalizing Drinfel'd's theory of Poisson homogeneous spaces from groups to groupoids.Comment: 24 pages, LaTeX2e (minor corrections, added section at end), final version of paper to appear in J. Diff. Geo

Implication the observed ψ(3770)→ppˉπ0\psi(3770)\to p\bar{p}\pi^0 for studying the ppˉ→ψ(3770)π0p\bar{p}\to \psi(3770)\pi^0 process

We study the charmonium $p \bar{p} \to \psi(3770) \pi^0$ reaction using effective lagrangian approach where the contributions from well established $N^*$ states are considered, and all parameters are fixed in the process of $e^+e^- \to p \bar{p}\pi^0$ at center of mass energy $\sqrt{s} = 3.773$ GeV. The experimental data on the line shape of the mass distribution of the $e^+e^- \to p\bar{p}\pi^0$ can be well reproduced. Based on the studying of $e^+e^- \to p \bar{p}\pi^0$, the total and differential cross sections of the $p \bar{p} \to \psi(3770) \pi^0$ reaction are predicted. At the same time we evaluated also the cross sections of the $p \bar{p} \to \psi(3686) \pi^0$ reaction. It is shown that the contribution of nucleon pole to this reaction is largest close to the reaction threshold. However, the interference between nucleon pole and the other nucleon resonance can still change the angle distributions significantly. Those theoretical results may be test by the future experiments at \overline{\mbox{P}}ANDA.Comment: 8 pages, 10 figures, and 4 tables. More discussions added and typos corrected. Accepted by Eur. Phys. J.