Rationality, regularity, and C_2-cofiniteness

We demonstrate that, for vertex operator algebras of CFT type, C_2-cofiniteness and rationality is equivalent to regularity. For C_2-cofinite vertex operator algebras, we show that irreducible weak modules are ordinary modules and C_2-cofinite, V_L^+ is C_2-cofinite, and the fusion rules are finite.

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Bibliographische Detailangaben
Veröffentlicht in:	Transactions of the American Mathematical Society 2004-08, Vol.356 (8), p.3391-3402
Hauptverfasser:	Abe, Toshiyuki, Buhl, Geoffrey, Dong, Chongying
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Axioms Mathematical lattices Mathematical theorems Mathematical vectors Operator algebras Operator theory Vector spaces Vertices
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Beschreibung
Zusammenfassung:	We demonstrate that, for vertex operator algebras of CFT type, C_2-cofiniteness and rationality is equivalent to regularity. For C_2-cofinite vertex operator algebras, we show that irreducible weak modules are ordinary modules and C_2-cofinite, V_L^+ is C_2-cofinite, and the fusion rules are finite.
ISSN:	0002-9947 1088-6850
DOI:	10.1090/S0002-9947-03-03413-5