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Braid groups and left distributive operations


Author: Patrick Dehornoy
Journal: Trans. Amer. Math. Soc. 345 (1994), 115-150
MSC: Primary 08A50; Secondary 20F36
DOI: https://doi.org/10.1090/S0002-9947-1994-1214782-4
MathSciNet review: 1214782
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Abstract: The decidability of the word problem for the free left distributive law is proved by introducing a structure group which describes the underlying identities. This group is closely connected with Artin's braid group $ {B_\infty }$. Braid colourings associated with free left distributive structures are used to show the existence of a unique ordering on the braids which is compatible with left translation and such that every generator $ {\sigma _i}$ is preponderant over all $ {\sigma _k}$ with $ k > i$. This ordering is a linear ordering.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1214782-4
Keywords: Braid group, word problem, nonassociative algebras, free algebras
Article copyright: © Copyright 1994 American Mathematical Society

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