Related papers: Simple current extensions beyond semi-simplicity

For a simple real Jordan algebra $V,$ a family of bi-differential operators from $\mathcal{C}^\infty(V\times V)$ to $\mathcal{C}^\infty(V)$ is constructed. These operators are covariant under the rational action of the conformal group of…

This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple…

We show that in a weak globular $\omega$-category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a higher-dimensional generalisation of the Eckmann-Hilton…

We consider integrable, category O-modules of indecomposable symmetrizable Kac-Moody algebras. We prove that unique factorization of tensor products of irreducible modules holds in this category, upto twisting by one dimensional modules.…

Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…

The proofs of K. Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we formulate and prove a Weak Coherence Theorem without using Weierstrass' Preparation Theorem, but only with power series expansions:…

We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on…

We prove that if $V$ is a conical simple self-dual quasi-lisse vertex algebra and $M$ is an ordinary module then $\dim X_M=\dim X_V$. Hence, if moreover $X_V$ is irreducible then $X_M=X_V$. In particular, this applies to quasi-lisse simple…

We prove that the categories of weight modules over the simple $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator algebras at fractional admissible levels and central charges are rigid (and hence the categories of weight…

This paper begins with a brief survey of the period prior to and soon after the creation of the theory of vertex operator algebras (VOAs). This survey is intended to highlight some of the important developments leading to the creation of…

We provide examples of foliations on the complex projective plane $\CP^2$ carrying positive foliated harmonic currents whose supports coincide with singular Levi-flats which, in turn, can be chosen real-analytic (but non-algebraic) or…

We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep(O(\infty) (formally), Rep(O(N), Rep(Sp(N) or of one of its associated fusion categories. If the braiding is not…

In this short note, we observe that Theorem 3.1 in arXiv:1508.00682 for semiorthogonal indecomposability of the derived category of smooth DM stacks based on the canonical bundle can be extended to the case of projective varieties with…

This is the first paper of a three-part series in which we develop a theory of conformal blocks for $C_2$-cofinite vertex operator algebras (VOAs) that are not necessarily rational. The ultimate goal of this series is to prove a…

Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S.…

The Wess-Zumino-Witten model defined on the group SU(2) has a unique (non-trivial) simple current of conformal dimension k/4 for each level k. The extended algebra defined by this simple current is carefully constructed in terms of…

In this text, we recall some basics and results about complex geometry and currents in the complex scenario. Most of the results are classic and their evidence is not given here. On the other hand, we describe in detail some notions to help…

We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of braided tensor categories if, and only if, it is non-degenerate. This includes the case of semisimple modular tensor categories, but also…

Observable currents are spacetime local objects that induce physical observables when integrated on an auxiliary codimension one surface. Since the resulting observables are independent of local deformations of the integration surface, the…

Dave Benson conjectured in 2020 that if $G$ is a finite $2$-group and $V$ is an odd-dimensional indecomposable representation of $G$ over an algebraically closed field $\Bbbk$ of characteristic $2$, then the only odd-dimensional…