Lebesgue Measure Preserving Thompson Monoid and Its Properties of Decomposition and Generators

Authors

William Li, Stanford UniversityFollow

Abstract

This paper defines the Lebesgue measure preserving Thompson monoid, denoted by G, which is modeled on the Thompson group F except that the elements of G preserve the Lebesgue measure and can be non-invertible. The paper shows that any element of the monoid G is the composition of a finite number of basic elements of the monoid G and the generators of the Thompson group F. However, unlike the Thompson group F, the monoid G is not finitely generated. The paper then defines equivalence classes of the monoid G, use them to construct a monoid H that is finitely generated, and shows that the union of the elements of the monoid H is a set of equivalence classes, the union of which is G.

Author Bio

William Li is a rising freshman at Stanford University where he hopes to study symbolic systems. Will is a passionate math/CS researcher who works to promote science education and lead STEM outreach in underrepresented communities. Outside of science, Will is a nationally acclaimed debater who enjoys promoting tech policy.

Faculty Sponsor

Sergiy Merenkov

Recommended Citation

Li, William (2021) "Lebesgue Measure Preserving Thompson Monoid and Its Properties of Decomposition and Generators," Rose-Hulman Undergraduate Mathematics Journal: Vol. 22: Iss. 1, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss1/8