TITLE:
Study about Non-Linear Structures
AUTHORS:
Stéphane Le Corre
KEYWORDS:
Algebraic Structures, Geometrical Spaces, Projective Spaces, Non-Linear Structures (Space, Field and Group)
JOURNAL NAME:
Open Access Library Journal,
Vol.7 No.10,
October
30,
2020
ABSTRACT: This article proposes a new algebraic structure that goes beyond the vector space, named sector space. We show that this new space is associated with projective spaces as vector space is associated with affine spaces. Parallelly, we suggest two other algebraic structures which extend the notions of group and field. Notions of element not reducible to a point (extended object), of ternary structure (extension of the binary notion of the linear group) and of complementary association (bifocal construction and mixture) seem to be the keystone of this building. These structures are associated with invariance properties by translation, rotation and zoom.