Related papers: Cofiniteness conditions, projective covers and the…

Let A be a commutative ring with 1/2 in A. In this paper, we define new characteristic classes for finitely generated projective A-modules V provided with a non degenerate quadratic form. These classes belong to the usual K-theory of A.…

We define a graded twisted-coassociative coproduct on the tensor algebra $TW$ of any $\Z^n$-graded vector space $W$. If $W$ is the desuspension space $\da V$ of a graded vector space $V$, the coderivations (resp. quadratic ``degree 1''…

We introduce a general categorical framework for finiteness conditions that unifies classical notions such as Noetherianness, Artinianness, and various forms of topological compactness. This is achieved through the concept of…

Let $\mathbb V$ be an $\mathbb N$-graded $C_2$-cofinite vertex operator algebra (VOA), not necessarily rational or self-dual. Using a special case of the sewing-factorization theorem from [GZ25a], we show that the end $\mathbb…

We prove that for operator spaces $V$ and $W$, the operator space $V^{**}\otimes_h W^{**}$ can be completely isometrically embedded into $(V\otimes_h W)^{**}$, $\otimes_h$ being the Haagerup tensor product. It is also shown that, for exact…

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…

We show that C_2-cofiniteness is enough to prove a modular invariance property of vertex operator algebras without assuming the semisimplicity of Zhu algebra. For example, if a VOA V=\oplus_{m=0}^{\infty}V_m is C_2-cofinite, then the space…

We investigate finite non-Abelian simple groups $G$ for which the projective cover of the trivial module coincides with the permutation module on a subgroup and classify all cases unless $G$ is of Lie type in defining characteristic.

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V^G is regular. It is proved that every irreducible V^G-module occurs in an irreducible g-twisted V-module for some g in G. Moreover, the quantum…

The category of modules over a string algebra is equipped with a tensor product defined point-wise and arrow-wise in terms of the underlying quiver. In the present article we investigate how this tensor product interacts with the…

We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from representations of a simple vertex operator algebra…

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…

We construct a certain topological algebra $\Ext ^{\sharp}_{G ^{\vee}} X (\chi)$ from a Deligne-Langlands parameter space $X (\chi)$ attached to the group of rational points of a connected split reductive algebraic group $G$ over a…

Let $k$ be a field, and let $\mathcal{C}$ be a Cauchy complete $k$-linear braided category with finite dimensional morphism spaces and ${{\rm End}(\bf 1)}=k$. We call an indecomposable object $X$ of $\mathcal C$ non-negligible if there…

We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C-bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky. We then provide a…

For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all…

For coprime $p,q\in\mathbb{Z}_{\geq 2}$, the triplet vertex operator algebra $W_{p,q}$ is a non-simple extension of the universal Virasoro vertex operator algebra of central charge $c_{p,q}=1-\frac{6(p-q)^2}{pq}$, and it is a basic example…

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and…

For any nullity $2$ extended affine Lie algebra $\mathcal{E}$ of maximal type and $\ell\in\mathbb{C}$, we prove that there exist a vertex algebra $V_{\mathcal{E}}(\ell)$ and an automorphism group $G$ of $V_{\mathcal{E}}(\ell)$ equipped with…

Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…