Regular Article - Theoretical Physics
On the structure constants of volume preserving diffeomorphism algebra
Department of Natural Science, Faculty of Education, Hirosaki University, Bunkyo-cho 1, Hirosaki, Aomori, 036-8560, Japan
* e-mail: email@example.com
Accepted: 28 April 2014
Published online: 20 May 2014
Regularizing a volume preserving diffeomorphism (VPD) is equivalent to a long standing problem, namely regularizing a Nambu–Poisson bracket. In this paper, as a first step toward regularizing VPD, we find general complete independent bases of VPD algebra. Especially, we find a complete independent basis that gives simple structure constants, where three area preserving diffeomorphism algebras are manifest. This implies that an algebra that regularizes a VPD algebra should include three Lie algebras.
© SIF and Springer-Verlag Berlin Heidelberg, 2014