The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm

 Access to full text

 Full (PDF)

1. [1] Artin E., Theorie der Zöpfe, Abh. Math. Sem. Univ. Hamburg, 1925, 4(1), 47–72 http://dx.doi.org/10.1007/BF02950718 Zbl51.0450.01
2. [2] Birman J.S., Braids, Links, and Mapping Class Groups, Ann. of Math. Stud., 82, Princeton University Press, Princeton, 1974 
3. [3] Brieskorn E., Automorphic sets and braids and singularities, In: Braids, Santa Cruz, July 13–26, 1986, Contemp. Math., 78, American Mathematical Society, Providence, 1988, 45–115 
4. [4] Burckel S., The wellordering on positive braids, J. Pure Appl. Algebra, 1997, 120(1), 1–17 http://dx.doi.org/10.1016/S0022-4049(96)00072-2 Zbl0958.20032
5. [5] Dehornoy P., Braid groups and left distributive operations, Trans. Amer. Math. Soc., 1994, 345(1), 115–150 http://dx.doi.org/10.1090/S0002-9947-1994-1214782-4 Zbl0837.20048
6. [6] Dehornoy P., Braids and Self-Distributivity, Progr. Math., 192, Birkhäuser, Basel, 2000 http://dx.doi.org/10.1007/978-3-0348-8442-6 
7. [7] Dehornoy P., Dynnikov I., Rolfsen D., Wiest B., Why are Braids Orderable?, Panor. Syntheses, 14, Société Mathématique de France, Paris, 2002 Zbl1048.20021
8. [8] Fenn R., Rourke C., Racks and links in codimension two, J. Knot Theory Ramifications, 1992, 1(4), 343–406 http://dx.doi.org/10.1142/S0218216592000203 Zbl0787.57003
9. [9] Hurwitz A., Ueber Riemann’sche Flächen wit gegebenen Verzweigungspunkten, Math. Ann., 1891, 39(1), 1–60 http://dx.doi.org/10.1007/BF01199469 
10. [10] Joyce D., A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra, 1982, 23(1), 37–65 http://dx.doi.org/10.1016/0022-4049(82)90077-9 Zbl0474.57003
11. [11] Kunen K., Elementary embeddings and infinitary combinatorics, J. Symbolic Logic, 1971, 36(3), 407–413 http://dx.doi.org/10.2307/2269948 Zbl0272.02087
12. [12] Larue D.M., Braid words and irreflexivity, Algebra Universalis, 1994, 31(1), 104–112 http://dx.doi.org/10.1007/BF01188182 Zbl0793.08007
13. [13] Laver R., A division algorithm for the free left distributive algebra, In: Logic Colloquium’ 90, Helsinki, July 15–22, 1990, Lecture Notes Logic, 2, Springer, Berlin, 1993, 155–162 Zbl0809.08004
14. [14] Laver R., The left distributive law and the freeness of an algebra of elementary embeddings, Adv. Math., 1992, 91(2), 209–231 http://dx.doi.org/10.1016/0001-8708(92)90016-E Zbl0822.03030
15. [15] Laver R., On the algebra of elementary embeddings of a rank into itself, Adv. Math., 1995, 110(2), 334–346 http://dx.doi.org/10.1006/aima.1995.1014 Zbl0822.03031
16. [16] Laver R., Braid group actions on left distributive structures, and well orderings in the braid groups, J. Pure Appl. Algebra, 1996, 108(1), 81–98 http://dx.doi.org/10.1016/0022-4049(95)00147-6 Zbl0859.20029
17. [17] Laver R., Miller S.K., Left division in the free left distributive algebra on one generator, J. Pure Appl. Algebra, 2010, 215(3), 276–282 http://dx.doi.org/10.1016/j.jpaa.2010.04.019 Zbl1208.08003
18. [18] Laver R., Moody J.A., Well-foundedness conditions connected with left-distributivity, Algebra Univsersalis, 2002, 47(1), 65–68 http://dx.doi.org/10.1007/s00012-002-8175-2 Zbl1058.20055
19. [19] Miller S.K., Free Left Distributive Algebras, PhD thesis, University of Colorado, Boulder, 2007 
20. [20] Miller S.K., Free left distributive algebras on κ generators (in preparation)