Publicação

Growths of endomorphisms of finitely generated semigroups

Detalhes bibliográficos
Resumo:	This paper studies the growths of endomorphisms of finitely generated semigroups. The growth is a certain dynamical characteristic describing how iterations of the endomorphism ‘stretch’ balls in the Cayley graph of the semigroup. We make a detailed study of the relation of the growth of an endomorphism of a finitely generated semigroup and the growth of the restrictions of the endomorphism to finitely generated invariant subsemigroups. We also study the possible values endomorphism growths can attain. We show the role of linear algebra in calculating the growths of endomorphisms of homogeneous semigroups. Proofs are a mixture of syntactic algebraic rewriting techniques and analytical tricks. We state various problems and suggestions for future research.
Autores principais:	Cain, Alan J.
Outros Autores:	Maltcev, Victor
Assunto:	Cayley graph endomorphism finitely generated semigroups growth General Mathematics
Ano:	2017
País:	Portugal
Tipo de documento:	artigo
Tipo de acesso:	acesso aberto
Instituição associada:	Universidade Nova de Lisboa
Idioma:	inglês
Origem:	Repositório Institucional da UNL

Descrição
Resumo:	This paper studies the growths of endomorphisms of finitely generated semigroups. The growth is a certain dynamical characteristic describing how iterations of the endomorphism ‘stretch’ balls in the Cayley graph of the semigroup. We make a detailed study of the relation of the growth of an endomorphism of a finitely generated semigroup and the growth of the restrictions of the endomorphism to finitely generated invariant subsemigroups. We also study the possible values endomorphism growths can attain. We show the role of linear algebra in calculating the growths of endomorphisms of homogeneous semigroups. Proofs are a mixture of syntactic algebraic rewriting techniques and analytical tricks. We state various problems and suggestions for future research.