Communications in Mathematical Physics

, Volume 214, Issue 2, pp 469–491 | Cite as

Extended Diffeomorphism Algebras¶and Trajectories in Jet Space

  • T. A. Larsson


Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra¶DRO(N) be the extension of diff(N)⊕ diff(1) by its four inequivalent Virasoro-like cocycles. Here diff(N) is the diffeomorphism algebra in N-dimensional spacetime and diff(1) describes reparametrizations of trajectories in the space of tensor-valued p-jets. DRO(N) has a Fock module for each p and each representation of gl(N). Analogous representations for gauge algebras (higher-dimensional Kac–Moody algebras) are also given. The reparametrization symmetry can be eliminated by a gauge fixing procedure, resulting in previously discovered modules. In this process, two DRO(N) cocycles transmute into anisotropic cocycles for diff(N). Thus the Fock modules of toroidal Lie algebras and their derivation algebras are geometrically explained.


Gauge Algebra Analogous Representation Moody Algebra Derivation Algebra Reparametrization Symmetry 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • T. A. Larsson
    • 1
  1. 1.Vanadisvägen 29, 113 23 Stockholm, Sweden.¶E-mail: tal@hdd.seSE

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