Principle Of Relativity And The Kinematics

Beginning with the principle of relativity,we study the general transformation for inertia reference frames.The Umov-Weyl-Fock-Hua transformation has been obtained.To make the dimensions of transformed coordinates to be consistent with those of original coordinates,the universal constants(c,l) should be introduced.The Umov-Wely-Fock-Hua transformations with two universal constants(c,l) form inertia motion transformation group IM(4).As the subgroup of IM(4),the possible kinematics groups with ten infinitesimal generators have SO(3) subgroup.We Study the possible kinematics groups and their algebras.The second Poincar(?) algebra,second Galilei algebra and second Carroll algebra,which has been ignored,has also been studied.We have found there exist some relations among the relativity algebras-dS algebra so(1,4),AdS algebra so(2,3) and Poincar(?) algebras iso(1,3).As the representation of isotropy algebra so(1,3),the generators of dS algebra so(1,4) plus that of AdS algebra so(2,3) lead to the generators of Poincar(?) algebra iso(1,3).There also exist the similar relations among the geometry kinematics algebras.As the representation of isotropy algebra so(4),the generators of Riemann sphere algebra so(5) plus that of Lobachevsky algebra so(4,1) lead to the generators of Euclid algebra iso(4).There also exist some relations among non-relativity algebras.These relations among the kinematics algebras are very different from the contractions and deformations.