INTRODUCTION TO AN ALGEBRAIC THEORY OF ARROWS, II

Abstract

This paper represents the second part of the article [1] under the same title published some years ago in this Annual, in which an algebraic theory of arrows or sliding vectors has been proposed, based on the axiomatically defined real standard vectors. Meanwhile the author has proposed a complex version [2] of the real standard vector spaces and has developed the corresponding complex version [3] of the real 3-dimensional linear analytic geometry [4]. This paper represents a complex version 'of the constructions exposed in [1]. As it is well known, the traditional mechanical interpritation of the real sliding vectors are the concentrated forces in analytical statics and analytical dynamics. The possibility of defining complex arrows has far reaching consequences. Its main result consists in the potenciality to develop a complex analytical mechanics with all the after-effects this fact implies for the logical foundations of this science and for the solution of Hilbert's sixth problem concerning its axiomatical consolidation.