Abstract
We define chirality in the context of chiral algebra. We show that it coincides with the more general chirality definition that appears in the literature, which does not require the existence of a quadratic space. Neither matrix representation of the orthogonal group nor complex numbers are used.
Highlights
Introduction to Symmetry and ChiralityCitation: Petitjean, M
The reflections are sequentially grouped into n/2 pairs, so that each of these pairs of reflections generates a rotation because their two supporting basis vectors have their squares with the same sign
In the case of the Lorentz group, it means that PT is classified as an indirect isometry
Summary
A mathematical definition of symmetry can be found in [7] It works in many cases, such as for geometric figures (with or without colors, as encountered in arts), for functions, probability distributions, graphs, matrices, strings, etc. This definition assumed the existence of a metric, but none of the axioms defining a true metric was necessary to define isometries. The definition of direct and indirect symmetries which is retained here in Definition 3, is not the classical one related to orientation preserving operators It is a more general one [9], which recovers the classical one in the case of Euclidean spaces.
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