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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 17410, 17 pages

Transformation groups on real plane and their differential invariants

Department of Applied Research, Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv 4 01601, Ukraine

Received 3 April 2006; Revised 29 June 2006; Accepted 9 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Complete sets of bases of differential invariants, operators of invariant differentiation, and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.