The sh Lie structure of Poisson brackets in field theory

A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.Comment: 24 pages Latex fil

Algebra Structures on Hom(C,L)

We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C,L) fail to hold. We define the concept of twisted domain (TD) algebras in order to recover the symmetries and also construct a modified Chevalley-Eilenberg complex in order to define the cohomology of such algebras

The Dynamical State of Barnard 68: A Thermally Supported, Pulsating Dark Cloud

We report sensitive, high resolution molecular-line observations of the dark cloud Barnard 68 obtained with the IRAM 30-m telescope. We analyze spectral-line observations of C18O, CS(2--1), C34S(2--1), and N2H+(1--0) in order to investigate the kinematics and dynamical state of the cloud. We find extremely narrow linewidths in the central regions of the cloud. These narrow lines are consistent with thermally broadened profiles for the measured gas temperature of 10.5 K. We determine the thermal pressure to be a factor 4 -- 5 times greater than the non-thermal (turbulent) pressure in the central regions of the cloud, indicating that thermal pressure is the primary source of support against gravity in this cloud. This confirms the inference of a thermally supported cloud drawn previously from deep infrared extinction measurements. The rotational kinetic energy is found to be only a few percent of the gravitational potential energy, indicating that the contribution of rotation to the overall stability of the cloud is insignificant. Finally, our observations show that CS line is optically thick and self-reversed across nearly the entire projected surface of the cloud. The shapes of the self-reversed profiles are asymmetric and are found to vary across the cloud in such a manner that the presence of both inward and outward motions are observed within the cloud. Moreover, these motions appear to be globally organized in a clear and systematic alternating spatial pattern which is suggestive of a small amplitude, non-radial oscillation or pulsation of the outer layers of the cloud about an equilibrium configuration.Comment: To appear in the Astrophysical Journal; 23 pages, 8 figures; Manuscript and higher resolution images can be obtained at http://cfa-www.harvard.edu/~ebergin/pubs_html/b68_vel.htm

Deformations of coisotropic submanifolds for fibrewise entire Poisson structures

We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the $L_\infty$-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo-Felder. In the symplectic case, we recover results previously obtained by Oh-Park. Moreover we consider the extended deformation problem and prove its obstructedness

NGC 2362: a Template for Early Stellar Evolution

We present UBVRI photometry for the young open cluster NGC 2362. From analysis of the appropriate color-color and color-magnitude diagrams we derive the fundamental parameters of the NGC 2362 cluster to be: age = 5 (+1-2) Myr, distance = 1480 pc, E(B-V)=0.10 mag. The cluster age was independently determined for both high mass (2.1 - 36Msun) and low mass (0.7 - 1.2Msun) stars with excellent agreement between the ages derived using post-main sequence and pre-main sequence evolutionary tracks for the high and low mass stars respectively. Analysis of this cluster's color-magnitude diagram reveals a well defined pre-main sequence (covering DeltaV ~ 9 magnitudes in V and extending from early A stars to near the hydrogen burning limit) which makes this cluster an ideal laboratory for pre-main sequence evolution studies.Comment: 9 pages, 3 figures, to be published in ApJ

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

The Dynamical State fo the Starless Dense Core FeSt 1-457: A Pulsating Globule?

High resolution molecular line observations of CS, HCO+, C18O and N2H+ were obtained toward the starless globule FeSt 1-457 in order to investigate its kinematics and chemistry. The HCO+ and CS spectra show clear self-reversed and asymmetric profiles across the face of the globule. The sense of the observed asymmetry is indicative of the global presence of expansion motions in the outer layers of the globule. These motions appear to be subsonic and significantly below the escape velocity of the globule. Comparison of our observations with near-infrared extinction data indicate that the globule is gravitationally bound. Taken together these considerations lead us to suggest that the observed expansion has its origin in an oscillatory motion of the outer layers of the globule which itself is likely in a quasi-stable state near hydrostatic equilibrium. Analysis of the observed linewidths of CO and N2H+ confirm that thermal pressure is the dominant component of the cloud's internal support. A simple calculation suggests that the dominant mode of pulsation would be an l = 2 mode with a period of 0.3 Myr. Deformation of the globule due to the large amplitude l = 2 oscillation may be responsible for the double-peaked structure of the core detected in high resolution extinction maps. Detailed comparison of the molecular-line observations and extinction data provides evidence for significant depletion of C18O and perhaps HCO+ while N2H+ may be undepleted to a cloud depth of about 40 magnitudes of visual extinction.Comment: to appear in ApJ vol 665 20 August 2007