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Published in:
2008 | OriginalPaper | Chapter
Diagram Rewriting for Orthogonal Matrices: A Study of Critical Peaks
Authors : Yves Lafont, Pierre Rannou
Published in: Rewriting Techniques and Applications
Publisher: Springer Berlin Heidelberg
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Orthogonal diagrams
represent decompositions of isometries of ℝ
n
into symmetries and rotations. Some convergent (that is noetherian and confluent) rewrite system for this structure was introduced by the first author. One of the rules is similar to Yang-Baxter equation. It involves a map
h
: ]0,
π
[
3
→]0,
π
[
3
.
In order to obtain the algebraic properties of
h
, we study the confluence of critical peaks (or critical pairs) for our rewrite system. For that purpose, we introduce
parametric diagrams
describing the calculation of angles of rotations generated by rewriting. In particular, one of those properties is related to the
tetrahedron equation
(also called Zamolodchikov equation).