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152
Quantum Geometry of Isolated Horizons and Black Hole Entropy
, 2000
"... Using the classical Hamiltonian framework of [1] as the point of departure, we carry out a nonperturbative quantization of the sector of general relativity, coupled to matter, admitting nonrotating isolated horizons as inner boundaries. The emphasis is on the quantum geometry of the horizon. Polym ..."
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Cited by 72 (4 self)
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Using the classical Hamiltonian framework of [1] as the point of departure, we carry out a nonperturbative quantization of the sector of general relativity, coupled to matter, admitting nonrotating isolated horizons as inner boundaries. The emphasis is on the quantum geometry of the horizon. Polymer excitations of the bulk quantum geometry pierce the horizon endowing it with area. The intrinsic geometry of the horizon is then described by the quantum ChernSimons theory of a U(1) connection on a punctured 2sphere, the horizon. Subtle mathematical features of the quantum ChernSimons theory turn out to be important for the existence of a coherent quantum theory of the horizon geometry. Heuristically, the intrinsic geometry is flat everywhere except at the punctures. The distributional curvature of the U(1) connection at the punctures gives rise to quantized deficit angles which account for the overall curvature. For macroscopic black holes, the logarithm of the number of these horizon microstates is proportional to the area, irrespective of the values of (nongravitational) charges. Thus, the black hole entropy can be accounted for entirely by the quantum states of the horizon geometry. Our analysis is applicable to all nonrotating black holes, including the astrophysically interesting ones which are very far from extremality. Furthermore, cosmological horizons (to which statistical mechanical considerations are known to apply) are naturally incorporated. An effort has been made to make the paper selfcontained by including short reviews of the background material.
TFT CONSTRUCTION OF RCFT CORRELATORS V: PROOF OF MODULAR INVARIANCE AND FACTORISATION
, 2005
"... The correlators of twodimensional rational conformal field theories that are obtained in the TFT construction of [I, II, IV] are shown to be invariant under the action of the relative modular group and to obey bulk and boundary factorisation constraints. We present results both for conformal field ..."
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Cited by 53 (33 self)
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The correlators of twodimensional rational conformal field theories that are obtained in the TFT construction of [I, II, IV] are shown to be invariant under the action of the relative modular group and to obey bulk and boundary factorisation constraints. We present results both for conformal field theories defined on oriented surfaces and for theories defined on unoriented surfaces. In the latter case, in particular the socalled cross cap constraint is included.
HomLie admissible Homcoalgebras and HomHopf algebras, Published as Chapter 17, pp 189206
 Generalized Lie theory in Mathematics, Physics and Beyond
, 2008
"... Abstract. The aim of this paper is to generalize the concept of Lieadmissible coalgebra introduced in [2] to Homcoalgebras and to introduce HomHopf algebras with some properties. These structures are based on the Homalgebra structures introduced in [12]. ..."
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Cited by 47 (14 self)
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Abstract. The aim of this paper is to generalize the concept of Lieadmissible coalgebra introduced in [2] to Homcoalgebras and to introduce HomHopf algebras with some properties. These structures are based on the Homalgebra structures introduced in [12].
HOMYANGBAXTER EQUATION, HOMLIE ALGEBRAS, AND QUASITRIANGULAR BIALGEBRAS
, 2009
"... We study a twisted version of the YangBaxter Equation, called the HomYangBaxter Equation (HYBE), which is motivated by HomLie algebras. Three classes of solutions of the HYBE are constructed, one from HomLie algebras and the others from Drinfeld’s (dual) quasitriangular bialgebras. Each solutio ..."
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Cited by 44 (18 self)
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We study a twisted version of the YangBaxter Equation, called the HomYangBaxter Equation (HYBE), which is motivated by HomLie algebras. Three classes of solutions of the HYBE are constructed, one from HomLie algebras and the others from Drinfeld’s (dual) quasitriangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group.
Notes on formal deformations of Homassociative and HomLie algebras
 Forum Math
, 2010
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Frobenius monads and pseudomonoids
 2CATEGORIES COMPANION 73
, 2004
"... Six equivalent definitions of Frobenius algebra in a monoidal category are provided. In a monoidal bicategory, a pseudoalgebra is Frobenius if and only i f it is star autonomous. Autonomous pseudoalgebras are also Frobenius. What i t means for a morphism of a bicategory to be a projective equivalenc ..."
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Cited by 39 (3 self)
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Six equivalent definitions of Frobenius algebra in a monoidal category are provided. In a monoidal bicategory, a pseudoalgebra is Frobenius if and only i f it is star autonomous. Autonomous pseudoalgebras are also Frobenius. What i t means for a morphism of a bicategory to be a projective equivalence is defined; this concept is related to &quot;strongly separable &quot; Frobenius algebras and &quot;weak monoidal Morita equivalence&quot;. Wreath products of Frobenius algebras are discussed.
Quantum geometry of algebra factorisations and coalgebra bundles
 Commun. Math. Phys
, 2000
"... We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices M2(C) = CZ2 · CZ2. We also further extend the coalgebra version of theory introduced previously, to include frame bundles and el ..."
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Cited by 36 (14 self)
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We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices M2(C) = CZ2 · CZ2. We also further extend the coalgebra version of theory introduced previously, to include frame bundles and elements of Riemannian geometry. As an example, we construct qmonopoles on all the Podle´s quantum spheres S 2 q,s. 1.
QUANTUM AND BRAIDED GROUP RIEMANNIAN GEOMETRY
, 1997
"... We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a selfdual manner as a principal bundle frame resolution and a dual pair of canonical forms. The role of LeviCivita connectio ..."
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Cited by 33 (17 self)
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We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a selfdual manner as a principal bundle frame resolution and a dual pair of canonical forms. The role of LeviCivita connection is naturally generalised to connections with vanishing torsion and cotorsion, which we introduce. We then provide the corresponding quantum group and braided group formulations with the universal quantum differential calculus. We also give general constructions for examples, including quantum spheres and quantum planes.
Are we at the dawn of quantumgravity phenomenology
 Lect. Notes Phys
, 2000
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