On the classification of modular fusion algebras

DOI10.1007/BF02101810zbMath0884.17018arXivhep-th/9408160MaRDI QIDQ1901799

Wolfgang Eholzer

Publication date: 1 April 1998

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9408160

zbMATH Keywords

irreducible representationsrational conformal field theoriesVerlinde's formulastrongly-modular fusion algebras

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Relationship to Lie algebras and finite simple groups (11F22) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items (16)

Modular data: the algebraic combinatorics of conformal field theory ⋮ Torus bundles not distinguished by TQFT invariants. With an appendix by Louis Funar and Andrei Rapinchuk ⋮ On the classification of the Grothendieck rings of non-self-dual modular categories ⋮ On classification of fermionic rational conformal field theories ⋮ Reconstruction of modular data from \(\mathrm{SL}_2(\mathbb{Z})\) representations ⋮ Fermion masses, critical behavior and universality ⋮ Pre-modular fusion categories of global dimension \(p^2\) ⋮ Constraints on extremal self-dual CFTs ⋮ Hopf algebras and congruence subgroups ⋮ Congruence subgroups and generalized Frobenius-Schur indicators ⋮ Congruence subgroups and super-modular categories ⋮ Hecke relations in rational conformal field theory ⋮ Holomorphic modular bootstrap revisited ⋮ On rational conformal field theories: explicit modular formulae ⋮ Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories ⋮ Modular categories with transitive Galois actions

Cites Work

• Unnamed Item
• Unnamed Item
• Fusion rules and modular transformations in 2D conformal field theory
• Rationality in conformal field theory
• Infinite conformal symmetry in two-dimensional quantum field theory
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• Die irreduziblen Darstellungen der Gruppen \(SL_2(Z_p)\), insbesondere \(SL_2(Z_2)\). I
• Meromorphic \(c=24\) conformal field theories
• Modular invariance and uniqueness of conformal characters
• FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP
• TOWARDS A CLASSIFICATION OF FUSION RULE ALGEBRAS IN RATIONAL CONFORMAL FIELD THEORIES
• On axiomatic approaches to vertex operator algebras and modules

This page was built for publication: On the classification of modular fusion algebras