DESCRIPTIONS OF THE SYSTEM OF GENERATORS OF SKEW FIELDS OF DIFFERENTIAL RATIONAL FUNCTIONS WITH INVARIANT QUATERNION OF VARIABLES UNDER THE ACTION OF A COMPACT SYMPLECTIC GROUP
Keywords:
differential invariant, quaternion, skew-field, non-commutative, group action, generating systemAbstract
In this paper, it is given in explicit form by the system of generators of the skew-field of invariant non-commutative differential rational functions with respect to the action of the group of compact symplectic transformations of a one-dimensional quaternion space, using the classical methods of invariance theory. The relationship between symmetric, skew-symmetric forms of real variables and hermitic forms of quaternionic variables, as well as some of their properties, are also shown and proved.
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