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.
Professor Sergiy Merenkov, Department of Mathematics, City College of New York
"Lebesgue Measure Preserving Thompson Monoid and Its Properties of Decomposition and Generators,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 22
, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss1/8