https://doi.org/10.1140/epjc/s10052-014-2878-3
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: msato@cc.hirosaki-u.ac.jp
Received:
4
April
2014
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
