We show that every injective homological ring epimorphism f : R → S where SR has flat dimension at most one gives rise to a 1cotilting R-module and we give sufficient conditions under which the converse holds true. Specializing to the case of a valuation domain R, we illustrate a bijective correspondence between equivalence classes of injective homological ring epimorphisms originating in R and...

The rational and C2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c̃ < 0 and C if c̃ = 0. If c̃ > 0, it is an extension of discrete Virasoro vertex operator algebra L(cp,q, 0) by its irreducible modules. It is also proved that for any rational and C2-cofinite sim...

We study the worst case complexity of regular operations on cofinite languages (i.e., languages whose complement is finite) and provide algorithms to compute efficiently the resulting minimal automata.

We investigate trace functions of modules for vertex operator algebras satisfying C2-cofiniteness. For the modular invariance property, Zhu assumed two conditions in [Zh]: A(V ) is semisimple and C2-cofiniteness. We show that C2cofiniteness is enough to prove a modular invariance property. For example, if a VOA V = ⊕m=0Vm is C2-cofinite, then the space spanned by generalized characters (pseudo-...

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be group, and let T:= Rep(G) the rigid C*-tensor category of continuous unitary representations G. Mod(T) C*-2-category cofinite semisimple finitely decomposable T-module categories. show that G-C*-algebras can identified with equivalence classes 1-morphisms out object T in Mod(T). For X: -> M1, Y: M2,...