Vines and partial transformations

• Autores: James East
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 216, Nº 2, 2007, págs. 787-810
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.06.005
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• Resumen

  • Abstract We introduce the partial vine monoid . This monoid is related to the partial transformation semigroup in the same way as the braid group is related to the symmetric group , and contains both the vine monoid [T.G. Lavers, The theory of vines, Comm. Algebra 25 (4) (1997) 1257¿1284] and the inverse braid monoid [D. Easdown, T.G. Lavers, The inverse braid monoid, Adv. Math. 186 (2) (2004) 438¿455]. We give a presentation for in terms of generators and relations, as well as a faithful representation in a monoid of endomorphisms of a free group. We also derive a new presentation for .