Communications in Mathematical Physics

, Volume 50, Issue 2, pp 167–175 | Cite as

A new method for constructing factorisable representations for current groups and current algebras

  • K. R. Parthasarathy
  • K. Schmidt
Article
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Abstract

LetC e ∞ (R n ,G) denote the group of infinitely differentiable maps fromn-dimensional Euclidean space into a simply connected and connected Lie group, which have compact support. This paper introduces a class of factorisable unitary representations ofC e ∞ (R n ,G) with the property that the unitary operatorU f corresponding to a functionf inC e ∞ (R n ,G) depends not only onf, but also on the derivatives off up to a certain order. In particular these representations can not be extended to the group of all continuous functions fromR n toG with compact support.

Keywords

Neural Network Statistical Physic Continuous Function Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • K. R. Parthasarathy
    • 1
  • K. Schmidt
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryEngland

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