Glasnik Matematicki, Vol. 43, No.1 (2008), 41-57.

VERTEX OPERATOR ALGEBRAS ASSOCIATED TO CERTAIN ADMISSIBLE MODULES FOR AFFINE LIE ALGEBRAS OF TYPE A

Ozren Perše

Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
e-mail: perse@math.hr

Abstract.   Let L(-(l+1)/2,0) be the simple vertex operator algebra associated to an affine Lie algebra of type Al(1) with the lowest admissible half-integer level -(l+1)/2, for even l. We study the category of weak modules for that vertex operator algebra which are in category O as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.

2000 Mathematics Subject Classification.   17B69, 17B67.

Key words and phrases.   Vertex operator algebra, affine Kac-Moody algebra, modular invariant representation.

Full text (PDF) (free access)

DOI: 10.3336/gm.43.1.05

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