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The Kauffman X-polynomial, also called the normalized bracket polynomial, is a 1-variable knot polynomial denoted X (Adams 1994, p. 153), L (Kauffman 1991, p. 33), or F ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

A semi-oriented 2-variable knot polynomial defined by F_L(a,z)=a^(-w(L))<|L|>, (1) where L is an oriented link diagram, w(L) is the writhe of L, |L| is the unoriented diagram ...

The commutation operation [a,b]=ab-ba corresponding to the Lie product.

The multiplication operation corresponding to the Lie bracket.

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

A smooth manifold with a Poisson bracket defined on its function space.

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

If g is a Lie algebra, then a subspace a of g is said to be a Lie subalgebra if it is closed under the Lie bracket. That is, a is a Lie subalgebra of g if for all x,y in a, ...

The span of an unoriented link diagram (also called the link spread) is the difference between the highest and lowest degrees of its bracket polynomial. The span is a ...