Symmetries of fluid dynamics with polytropic exponent

The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza-Klein type framework of Duval et al. In the standard polytropic case the recent results of O'Raifeartaigh and Sreedhar are confirmed. Similar results are proved for polytropic exponent gamma = -1, which corresponds to the dimensional reduction of d-branes. The relation between the duality transformation used in describing supernova explosion and cosmology is explained. (C) 2001 Elsevier Science B.V. All rights reserved.