Cofiniteness conditions, projective covers and the logarithmic tensor product theory

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dc.creatorHuang, Yi-Zhi
dc.date2007-12-26
dc.date.accessioned2026-07-07T08:51:19Z
dc.date.available2026-07-07T08:51:19Z
dc.descriptionWe construct projective covers of irreducible V-modules in the category of grading-restricted generalized V-modules when V is a vertex operator algebra satisfying the following conditions: 1. V is C_{1}-cofinite in the sense of Li. 2. There exists a positive integer N such that the differences between the real parts of the lowest conformal weights of irreducible V-modules are bounded by N and such that the associative algebra A_{N}(V) is finite dimensional. This result shows that the category of grading-restricted generalized V-modules is a finite abelian category over C. Using the existence of projective covers, we prove that if such a vertex operator algebra V satisfies in addition Condition 3, that irreducible V-modules are R-graded and C_{1}-cofinite in the sense of the author, then the category of grading-restricted generalized V-modules is closed under P(z)-tensor product operations for z in C^{\times}. We also prove that other conditions for applying the logarithmic tensor product theory developed by Lepowsky, Zhang and the author hold. Consequently, for such V, this category has a natural structure of braided tensor category. In particular, when $V$ is of positive energy and C_{2}-cofinite, Conditions 1--3 are satisfied and thus all the conclusions hold.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/0712.4109
dc.identifierhttp://arxiv.org/abs/0712.4109
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144899
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectRepresentation Theory
dc.subject17B69; 81T40; 18D10
dc.titleCofiniteness conditions, projective covers and the logarithmic tensor product theory
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