Publicación: BIANCHI SPACES AND THEIR THREE-DIMENSIONAL ISOMETRIES AS S-EXPANSIONS OF TWO-DIMENSIONAL ISOMETRIES
Fecha
2013
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Journal of Physics A-Mathematical and Theoretical
Resumen
IN THIS PAPER WE SHOW THAT SOME 3-DIMENSIONAL ISOMETRY ALGEBRAS, SPECIFICALLY THOSE OF TYPE I, II, III AND V (ACCORDING BIANCHI'S CLASSIFICATION), CAN BE OBTAINED AS EXPANSIONS OF THE ISOMETRIES IN 2 DIMENSIONS. IT IS SHOWN THAT IN GENERAL MORE THAN ONE SEMIGROUP WILL LEAD TO THE SAME RESULT. IT IS IMPOSSIBLE TO OBTAIN THE ALGEBRAS OF TYPE IV, VI-IX AS AN EXPANSION FROM THE ISOMETRY ALGEBRAS IN 2 DIMENSIONS. THIS MEANS THAT THE FIRST SET OF ALGEBRAS HAS PROPERTIES THAT CAN BE OBTAINED FROM ISOMETRIES IN 2 DIMENSIONS WHILE THE SECOND SET HAS PROPERTIES THAT ARE IN SOME SENSE INTRINSIC IN 3 DIMENSIONS. ALL THE RESULTS ARE CHECKED WITH COMPUTER PROGRAMS. THIS PROCEDURE CAN BE GENERALIZED TO HIGHER DIMENSIONS, WHICH COULD BE USEFUL FOR DIVERSE PHYSICAL APPLICATIONS.
