In this paper, we investigate the Lie algebra structures of weight one subspaces C2-cofinite vertex operator superalgebras. We also show that for any positive integer k, superalgebras Lsl(1|n+1)(k,0) and Losp(2|2n)(k,0) have inequivalent infinitely many irreducible admissible modules. As a consequence, give proof fact Lg(k,0) is if only g either simple algebra, or g=osp(1|2n), k nonnegative int...

Let R be a commutative noetherian ring and let $$\mathfrak {a}$$ an ideal of R. In this paper, we study certain condition, namely $$C_{\mathfrak {a}}$$ , introduced by Aghapournahr Melkersson, on the extension two subcategories R-modules. We develop some main results Yoshizawa (Proc Am Math Soc 140(7):2293–2305, 2012; J Commut Algebra 13:137–155, 2021). As example subcategories, weakly Laskeria...

Let V L and V R be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over V L ⊗ V . We prove that the qτ -qτ -traces (natural traces involving qτ = e2πiτ and qτ = e2πiτ ) of geometrically modified genus-zero correlation functions for F are convergent in suitable regions a...

Let R be a commutative Noetherian ring, a an ideal of R, and let M be a finitely generated R-module. For a non-negative integer t, we prove that H a(M) is a-cofinite whenever H t a(M) is Artinian and H i a(M) is a-cofinite for all i < t. This result, in particular, characterizes the a-cofiniteness property of local cohomology modules of certain regular local rings. Also, we show that for a loca...

In this paper, it is shown that the diagonal coset vertex operator algebra C(Lg(k+2,0),Lg(k,0)⊗Lg(2,0)) rational and C2-cofinite in case g=so(2n), n≥3 k an admissible number for gˆ. It also C(Lsl2(k+4,0),Lsl2(k,0)⊗Lsl2(4,0)) sl2ˆ. Furthermore, irreducible modules of are classified a positive odd integer.