The equation [B,(A-1)(A,B)] = 0 and virtual knots and links

Stephen Budden, and Roger Fenn. "The equation [B,(A-1)(A,B)] = 0 and virtual knots and links." Fundamenta Mathematicae 184.1 (2004): 19-29. <http://eudml.org/doc/283165>.

@article{StephenBudden2004,
abstract = {Let A, B be invertible, non-commuting elements of a ring R. Suppose that A-1 is also invertible and that the equation [B,(A-1)(A,B)] = 0 called the fundamental equation is satisfied. Then this defines a representation of the algebra ℱ = A, B | [B,(A-1)(A,B)] = 0. An invariant R-module can then be defined for any diagram of a (virtual) knot or link. This halves the number of previously known relations and allows us to give a complete solution in the case when R is the quaternions.},
author = {Stephen Budden, Roger Fenn},
journal = {Fundamenta Mathematicae},
keywords = {switch; biquandle; virtual knot},
language = {eng},
number = {1},
pages = {19-29},
title = {The equation [B,(A-1)(A,B)] = 0 and virtual knots and links},
url = {http://eudml.org/doc/283165},
volume = {184},
year = {2004},
}

TY - JOUR
AU - Stephen Budden
AU - Roger Fenn
TI - The equation [B,(A-1)(A,B)] = 0 and virtual knots and links
JO - Fundamenta Mathematicae
PY - 2004
VL - 184
IS - 1
SP - 19
EP - 29
AB - Let A, B be invertible, non-commuting elements of a ring R. Suppose that A-1 is also invertible and that the equation [B,(A-1)(A,B)] = 0 called the fundamental equation is satisfied. Then this defines a representation of the algebra ℱ = A, B | [B,(A-1)(A,B)] = 0. An invariant R-module can then be defined for any diagram of a (virtual) knot or link. This halves the number of previously known relations and allows us to give a complete solution in the case when R is the quaternions.
LA - eng
KW - switch; biquandle; virtual knot
UR - http://eudml.org/doc/283165
ER -