caa a22 4500 606160744 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10468-015-9550-y doi (NATIONALLICENCE)springer-10.1007/s10468-015-9550-y Iterative Algebras [Elektronische Daten] [Jason Bell, Blake Madill] Given a finitely generated free monoid X and a morphism ϕ : X → X, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras can be easily characterized in terms of linear algebra and combinatorial data from the morphism and that, moreover, it is decidable whether or not an iterative algebra has these properties. Finally, we use our construction to answer several questions of Greenfeld, Leroy, Smoktunowicz, and Ziembowski by constructing a primitive graded nilpotent algebra with Gelfand-Kirillov dimension two that is finitely generated as a Lie algebra. Springer Science+Business Media Dordrecht, 2015 Graded nilpotent algebras nationallicence Monoids nationallicence Iterative algebras nationallicence Decidability nationallicence Lie algebras nationallicence Monomial algebras nationallicence Combinatorics on words nationallicence Morphic words nationallicence Bell Jason Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Madill Blake Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1533-1546 1386-923X 18:6<1533 2015 18 10468 https://doi.org/10.1007/s10468-015-9550-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9550-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bell Jason Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 700 1- Madill Blake Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1533-1546 1386-923X 18:6<1533 2015 18 10468