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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Braid groups and left distributive operations
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by Patrick Dehornoy PDF
Trans. Amer. Math. Soc. 345 (1994), 115-150 Request permission

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.
References
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • 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