By Winfried Kohnen, Rainer Weissauer
This e-book, a part of the sequence Contributions in Mathematical and Computational Sciences, stories fresh advancements within the conception of vertex operator algebras (VOAs) and their purposes to arithmetic and physics.
The mathematical concept of VOAs originated from the well-known giant moonshine conjectures of J.H. Conway and S.P. Norton, which envisioned a deep dating among the characters of the most important easy finite sporadic workforce, the Monster and the idea of modular kinds encouraged through the observations of J. MacKay and J. Thompson.
The contributions are according to lectures added on the 2011 convention on Conformal box conception, Automorphic types and comparable subject matters, prepared through the editors as a part of a distinct software provided at Heidelberg college that summer time below the sponsorship of the math heart Heidelberg (MATCH).
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Additional resources for Conformal Field Theory, Automorphic Forms and Related Topics: CFT, Heidelberg, September 19-23, 2011
Math. 18, 621–650 (2012) 56. : Modular invariance of vertex operator algebras satisfying C2 -cofiniteness. Duke Math. J. 122, 51–91 (2004) 57. : Flatness of tensor products and semi-rigidity for C2 -cofinite vertex operator algebras I. 1407 58. p/ and the restricted quantum group at root of unity. In: Exploring New Structures and Natural Constructions in Mathematical Physics. Advanced Studies in Pure Mathematics, vol. 61. Mathematical Society of Japan, Tokyo (2011). 4607 59. : A braided monoidal category for free super-bosons.
Commun. Math. Phys. 247(3), 713–742 (2004) 40. : An algebraic approach to logarithmic conformal field theory. In: Proceedings of the School and Workshop on Logarithmic Conformal Field Theory and its Applications (Tehran, 2001). Int. J. Mod. Phys. A 18, 4593–4638 (2003) 41. : A rational logarithmic conformal field theory. Phys. Lett. B 386, 131–137 (1996). hep-th/9606050 42. : A local logarithmic conformal field theory. Nucl. Phys. B 538, 631–658 (1999). hep-th/9807091 43. : From boundary to bulk in logarithmic CFT.
The Kazhdan-Lusztig correspondence for the representation category of the triplet W -algebra in logorithmic conformal field theories. (Russian) Teoret. Mat. Fiz. 148(3), 398–427 (2006) 32. : Logarithmic extensions of minimal models: characters and modular transformations. Nucl. Phys. B 757, 303–343 (2006) 33. : Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center. Commun. Math. Phys. 265, 47–93 (2006) 34. : Kazhdan–Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models.
Conformal Field Theory, Automorphic Forms and Related Topics: CFT, Heidelberg, September 19-23, 2011 by Winfried Kohnen, Rainer Weissauer