Knot polynomial identities and quantum group coincidences
نویسندگان
چکیده
منابع مشابه
Knot polynomial identities and quantum group coincidences
We construct link invariants using the D2n subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the D2n planar algebras. We discuss the origins of these ...
متن کاملThe Knot Group and The Jones Polynomial
In this thesis, basic knot theory is introduced, along with concepts from topology, algebra and algebraic topology, as they relate to knot theory. In the first chapter, basic definitions concerning knots are presented. In the second chapter, the fundamental group is applied as a method of distinguishing knots. In particular the torus knots are classified using the fundamental group, and a gener...
متن کاملRepresentations of the Symmetric Group and Polynomial Identities
Let Sn denote the symmetric group on n symbols. When F has characteristic zero or greater than n, the group algebra FSn is a direct sum of p(n) matrix algebras over F, where p(n) is the number of partitions of n. We present an efficient method due to J. M. Clifton (1981) that calculates the matrix associated to each element of Sn, for each partition of n. In 1950, A. I. Malcev and W. Specht ind...
متن کاملAlgebras, Dialgebras, and Polynomial Identities *
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting oper...
متن کاملPolynomial identities for partitions
For any partition λ of an integer n , we write λ =< 11, 22, . . . , nn > where mi(λ) is the number of parts equal to i . We denote by r(λ) the number of parts of λ (i.e. r(λ) = ∑n i=1mi(λ) ). Recall that the notation λ ` n means that λ is a partition of n . For 1 ≤ k ≤ N , let ek be the k-th elementary symmetric function in the variables x1, . . . , xN , let hk be the sum of all monomials of to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Quantum Topology
سال: 2011
ISSN: 1663-487X
DOI: 10.4171/qt/16