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

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Budden S., Fenn R.

Fundamenta Mathematicae

2004

tom 184

nr 1

19-29

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.

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1 Fundamenta Mathematicae

1 Budden S.

1 Fenn R.

1 2004

Wyniki wyszukiwania

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