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1991 Mathematics Subject assume automorphism Beijing bijective map bimodule block braid groups canonical China commutative conjugacy classes conjugate consider contains contradiction copairable Corollary defect group defined Definition denote Dept elements equivalent exists fiber fibrations fibrations of genus finite group finitely cogenerated GL(n graph group G Hence homomorphism Hopf invariant ideal idempotent implies indecomposable induced injective involution irreducible representations isomorphism Kac-Moody algebras Lemma Let G linearly compact Math Mathematics Subject Classification maximal set Moreover Morita duality morphism noetherian non-negligible singularities nonzero normal subgroup obtain p-group paper positive integer prime projective modules proof of Theorem Proposition prove quasi-finite rays resp result right congruence right Kasch duality satisfies Section set of rank simple groups Sn(F soluble structure subgroup of G submodule subset Suppose symmetric matrices t-ideal torsion theory unique Univ universally Chinese vector vertex operator algebra zero ZG-submodule