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Mendes, S. & Bettencourt, G. H. (2019). Semigroup homomorphism generated by quasimorphism. VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM).
Export Reference (IEEE) 
S. M. Mendes and G. H. Bettencourt,  "Semigroup homomorphism generated by quasimorphism", in VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM), Covilhã, 2019
Export BibTeX 
@misc{mendes2019_1776125404620,
	author = "Mendes, S. and Bettencourt, G. H.",
	title = "Semigroup homomorphism generated by quasimorphism",
	year = "2019",
	howpublished = "Digital",
	url = "http://www.wcdanm-ubi19.uevora.pt/"
}
Export RIS 
TY  - CPAPER
TI  - Semigroup homomorphism generated by quasimorphism
T2  - VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM)
AU  - Mendes, S.
AU  - Bettencourt, G. H.
PY  - 2019
CY  - Covilhã
UR  - http://www.wcdanm-ubi19.uevora.pt/
AB  - Erschler and Karlsson [3] constructed a homomorphism from a finitely generated group to the reals through a random walk approach. In our previous work, similar results were obtained for a semidirect product using the word length [1]. In [2], the word length was replaced by a quasimorphism. It turns out that, working with quasimorphisms made it possible to generalize further the construction to an infinite, finitely generated semigroup S, endowed with a probability measure. Specifically, using semigroup quasimorphisms, we construct a homomorphism from S to (R,+).

[1]Bettencourt, G. and Mendes, S., Homomorphisms to R of semidirect products: a dynamical construction, Appl. Math. Inf. Sci., 9.6, 2015, pp. 1--7.
[2]Bettencourt, G. and Mendes, S., Homomorphisms to R generated by quasimorphisms,
Mediterr. J. Math., 13, 2016, pp. 3205--3219.
[3]Erschler, A., and Karlsson, A., Homomorphisms to R constructed from random walks,
Annales de l'Institut Fourier, 60.6, 2010, pp. 2095--2113.
ER  -