Symmetrization of Brace Algebras

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra

Sh-Lie algebras Induced by Gauge Transformations

The physics of ``particles of spin $\leq 2$'' leads to representations of a Lie algebra $\Xi$ of gauge parameters on a vector space $\Phi$ of fields. Attempts to develop an analogous theory for spin $>2$ have failed; in fact, there are claims that such a theory is impossible (though we have been unable to determine the hypotheses for such a `no-go' theorem). This led BBvD [burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent parameters' in a setting where some analysis in terms of smooth functions is possible. Having recognized the resulting structure as that of an sh-lie algebra ($L_\infty$-algebra), we have now reproduced their structure entirely algebraically, hopefully shedding some light on what is going on.Comment: Now 24 pages, LaTeX, no figures Extensively revised in terms of the applications and on shell aspects. In particular, a new section 8 analyzes Ikeda's 2D example from our perspective. His bracket is revealed as a generalized Kirillov-Kostant bracket. Additional reference

Noether's variational theorem II and the BV formalism

We review the basics of the Lagrangian approach to field theory and recast Noether's Second Theorem formulated in her language of dependencies using a slight modernization of terminology and notation. We then present the Cattaneo-Felder sigma model and work out the Noether identities or dependencies for this model. We review the description of the Batalin-Vilkovisky formalism and show explicitly how the anti-ghosts encode the Noether identities in this example.Comment: 15 pages, submitted to the Proceedings of the 2002 Winter School ``Geometry and Physics'', Srni, Czech Republi

Symmetrization of brace algebra

summary:Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on $\bigoplus_{k\ge 1}\operatorname{Hom}(V^{\otimes k},V)$ coincides with the natural symmetric brace structure on $\bigoplus_{k\ge 1}\operatorname{Hom}(V^{\otimes k},V)^{as}$, the direct sum of spaces of antisymmetric maps $V^{\otimes k}\to V$

Introduction to SH Lie algebras for physicists

Much of point particle physics can be described in terms of Lie algebras and their representations. Closed string field theory, on the other hand, leads to a generalization of Lie algebra which arose naturally within mathematics in the study of deformations of algebraic structures [SS]. It also appeared in work on higher spin particles [BBvD]. Representation theoretic analogs arose in the mathematical analysis of the Batalin-Fradkin-Vilkovisky approach to constrained Hamiltonians [S6]

Brown Dwarf Jets: Investigating the Universality of Jet Launching Mechanisms at the Lowest Masses

Recently it has become apparent that proto-stellar-like outflow activity extends to the brown dwarf (BD) mass regime. While the presence of accretion appears to be the common ingredient in all objects known to drive jets fundamental questions remain unanswered. The more prominent being the exact mechanism by which jets are launched, and whether this mechanism remains universal among such a diversity of sources and scales. To address these questions we have been investigating outflow activity in a sample of protostellar objects that differ considerably in mass and mass accretion rate. Central to this is our study of brown dwarf jets. To date Classical T Tauri stars (CTTS) have offered us the best touchstone for decoding the launching mechanism. Here we shall summarise what is understood so far of BD jets and the important constraints observations can place on models. We will focus on the comparison between jets driven by objects with central mass < 0.1M \odot and those driven by CTTSs. In particular we wish to understand how the the ratio of the mass outflow to accretion rate compares to what has been measured for CTTSs.Comment: Proceedings of IAU meeting 275, "Jets at All Scales