The Hilbert Modular Group and Orthogonal Groups
Adrian Hauffe-Waschb\"usch, Aloys Krieg

TL;DR
This paper establishes an explicit isomorphism between the Hilbert modular group and specific subgroups of the orthogonal group SO(2, 2), using linear algebra techniques tailored for number theory.
Contribution
It provides a novel explicit isomorphism linking Hilbert modular groups with orthogonal groups, enhancing understanding of their algebraic structures.
Findings
Explicit isomorphism between Hilbert modular group and SO(2, 2) subgroups
Application of linear algebra methods to number theory
New insights into the structure of congruence subgroups
Abstract
We derive an explicit isomorphism between the Hilbert modular group and certain congruence subgroups on the one hand and particular subgroups of the special orthogonal group on the other hand. The proof is based on an application of linear algebra adapted to number theoretical needs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Mathematics and Applications
