scholarly journals LOGARITHMIC KNOT INVARIANTS ARISING FROM RESTRICTED QUANTUM GROUPS

2008 ◽  
Vol 19 (10) ◽  
pp. 1203-1213 ◽  
Author(s):  
JUN MURAKAMI ◽  
KIYOKAZU NAGATOMO
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Field Theories ◽  
Projective Modules ◽  
Conformal Field Theories ◽  
Knot Invariants ◽  
Conformal Field ◽  
Alexander Invariants

We construct knot invariants from the radical part of projective modules of the restricted quantum group [Formula: see text] at [Formula: see text], and we also show a relation between these invariants and the colored Alexander invariants. These projective modules are related to logarithmic conformal field theories.

The contour picture of quantum groups: Conformal field theories

1991 ◽  
Vol 364 (1) ◽  
pp. 195-233 ◽  
Author(s):  
C. Ramirez ◽  
H. Ruegg ◽  
M. Ruiz-Altaba
Keyword(s):  
Quantum Groups ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

scholarly journals Quantum groups and conformal field theories

1989 ◽  
Vol 329 (1605) ◽  
pp. 343-347
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Theory ◽  
Conformal Field

Rational conformal field theories can be interpreted as defining quasi-triangular Hopf algebras. The Hopf algebra is determined by the duality properties of the conformal theory.

scholarly journals On Fusion Rules in Logarithmic Conformal Field Theories

1997 ◽  
Vol 12 (10) ◽  
pp. 1943-1958 ◽  
Author(s):  
Michael A. I. Flohr
Keyword(s):  
Quantum Group ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Group Representations ◽  
Fusion Rules ◽  
Conformal Field ◽  
Almost All

We find the fusion rules for the cp,1 series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance of negative fusion coefficients which can be understood in terms of exceptional quantum group representations. The effective fusion rules (i.e. without signs and multiplicities) resemble the BPZ fusion rules for the virtual minimal models with conformal grid given via c = c3p,3. This leads to the conjecture that (almost) all minimal models with c = cp,q, gcd (p,q) > 1, belong to the class of rational logarithmic conformal field theories.

RECONSTRUCTION THEOREMS AND RATIONAL CONFORMAL FIELD THEORIES

1991 ◽  
Vol 06 (24) ◽  
pp. 4359-4374 ◽  
Author(s):  
SHAHN MAJID
Keyword(s):  
Fourier Transform ◽  
Quantum Group ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Generalized Fourier Transform ◽  
Conformal Field ◽  
Reconstruction Theorem

We obtain an explicit reconstruction theorem for rational conformal field theories and other situations where we are presented with a braided or quasitensor category [Formula: see text]. It takes the form of a generalized Fourier transform. The reconstructed object turns out to be a quantum group in a generalized sense. Our results include both the Tannaka-Krein case where there is a functor [Formula: see text], and the case where there is no functor at all.

scholarly journals A PLANAR ALGEBRA CONSTRUCTION OF THE HAAGERUP SUBFACTOR

2010 ◽  
Vol 21 (08) ◽  
pp. 987-1045 ◽  
Author(s):  
EMILY PETERS
Keyword(s):  
Quantum Groups ◽  
Finite Depth ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Planar Algebra

Most known examples of subfactors occur in families, coming from algebraic objects such as groups, quantum groups and rational conformal field theories. The Haagerup subfactor is the smallest index finite depth subfactor which does not occur in one of these families. In this paper we construct the planar algebra associated to the Haagerup subfactor, which provides a new proof of the existence of the Haagerup subfactor. Our technique is to find the Haagerup planar algebra as a singly generated subfactor planar algebra, that is contained inside a graph planar algebra.

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