2005/05/04 by Atsushi Matsuo, Matsuo, Atsushi, Kiyokazu Nagatomo +3 · 3 citations
Mathematics · #13J99 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:13J99 #msc:17B69
paper · pdf · doi:10.48550/arxiv.math/0505071
41 pages
arxiv created 2005/05/04 · openalex publication_date 2005/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced and various module categories over quasi-finite algebras are described. When applied to the current algebras (universal enveloping algebras) of vertex operator algebras satisfying Zhu's C2-finiteness condition, our general consideration derives important consequences on representation theory of such vertex operator algebras. In particular, the category of modules over such a vertex operator algebra is shown to be equivalent to the category of modules over a finite-dimensional associative algebra.