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...

Classical tilting theory generalizes Morita theory of equivalence of module categories. The key property – existence of category equivalences between large full subcategories of the module categories – forces the representing tilting module to be finitely generated. However, some aspects of the classical theory can be extended to infinitely generated modules over arbitrary rings. In this paper,...

We show that there is a braided tensor category structure on the of C 1 -cofinite modules for (universal or simple) Virasoro vertex operator algebras arbitrary central charge. In generic case charge c = 13 − 6 ( t + ) , with ∉ Q we prove semisimplicity, rigidity and non-degeneracy also compute fusion rules this category.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

It is shown that any simple, rational and C2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c = 1, is isomorphic to L(12 , 0) ⊗ L( 1 2 , 0). 2000MSC:17B69

Does a given a set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this problem. However, we present an algorithm for testing whether the complement of a finite region is tileable by a set of rectangles.

We consider the notion of randomness relative to an oracle: a real number is random in A if and only if its initial segments are algorithmically incompressible in a self-delimiting universal machine equipped with an oracle A. We prove that the probability that a program for infinite computations outputs a cofinite set is random in the second jump of the halting problem.