Morita classes of algebras in modular tensor categories

• Autores: Liang Kong, Ingo Runkel
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 5, 2008, págs. 1548-1576
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.07.004
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• Resumen

  • We consider algebras in a modular tensor category . If the trace pairing of an algebra A in is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category . We prove that two simple algebras with non-degenerate trace pairing are Morita-equivalent if and only if their full centres are isomorphic as algebras. This result has an interesting interpretation in two-dimensional rational conformal field theory; it implies that there cannot be several incompatible sets of boundary conditions for a given bulk theory