THE ALEXANDER AND JONES POLYNOMIALS THROUGH REPRESENTATIONS OF ROOK ALGEBRAS
نویسندگان
چکیده
منابع مشابه
The Alexander and Jones Polynomials Through Representations of Rook Algebras
In the 1920’s Artin defined the braid group, Bn, in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most ...
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Let n be a positive integer and let n = {1, . . . , n}. Let R be the set of all oneto-one maps σ with domain I (σ ) ⊆ n and range J (σ) ⊆ n. If i ∈ I (σ ) let iσ denote the image of i under σ . There is an associative product (σ, τ ) → στ on R defined by composition of maps: i(στ)= (iσ )τ if i ∈ I (σ ) and iσ ∈ I (τ ). Thus the domain I (στ) consists of all i ∈ I (σ ) such that iσ ∈ I (τ ). The...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2012
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216512501143