2020/05/28 by Dražen Adamović, Adamovic, Drazen, Ante Čeperić +1
Mathematics · #17B69 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2005.13842
openalex publication_date 2020/05/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, we study the family of vertex operator algebras SF(d)+,\nknown as symplectic fermions. This family is of a particular interest because\nthese VOAs are irrational and C2-cofinite.\n We determine the Zhu's algebra A(SF(d)+) and show that the equality of\ndimensions of A(SF(d)+) and the C2--algebra mathcal P(SF(d)+) holds\nfor d \≥ 2 (the case of d=1 was treated by T. Abe). We use these results\nto prove a conjecture by Y. Arike and K. Nagatomo on the dimension of the space\nof one-point functions on SF(d)+.\n