3.8 Proceedings Paper

CAYLEY MAP FOR SYMPLECTIC GROUPS

Publisher

INST BIOPHYSICS & BIOMEDICAL ENGINEERING BULGARIAN ACAD SCIENCES
DOI: 10.7546/giq-22-2021-154-164

Keywords

Cayley formula; Cayley map; group composition; Hamiltonian matrices; Lie algebra; Lie group; rotations; symmetric matrices; symplectic matrices; vector parameterization

Ask authors/readers for more resources

Despite their importance, symplectic groups are not as popular as orthogonal groups possibly due to their more complex algebraic structures. However, it has been shown that in some sense symplectic groups can be represented by even dimensional symmetric matrices.
Despite of their importance, the symplectic groups are not so popular like orthogonal ones as they deserve. The only explanation of this fact seems to be that their algebras can not be described so simply. While in the case of the orthogonal groups they are just the anti-symmetric matrices, those of the symplectic ones should be split in four blocks that have to be specified separately. It turns out however that in some sense they can be presented by the even dimensional symmetric matrices. Here, we present such a scheme and illustrate it in the lowest possible dimension via the Cayley map. Besides, it is proved that by means of the exponential map all such matrices generate genuine symplectic matrices.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

3.8
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available