arXiv subjects
Publications and source records attributed to Juan Villarreal.
This work is motivated by recent developments in celestial holography. In \cite{CP}, the authors interpreted QCD collinear singularities in terms of operator product expansions in a two-dimensional CFT. We reformulate the algebraic structures arising in their work using the formalism of non-linear Lie conformal algebras developed in \cite{SK}.
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 affine vertex algebras $L_{k}(\mathfrak{g})$. For admissible $k$ it reproves a result in \cite{A2}, and it further extends it to non-admissible levels.
Logarithmic vertex algebras were introduced in our previous paper, motivated by logarithmic conformal field theory. Non-local Poisson vertex algebras were introduced by De Sole and Kac, motivated by the theory of integrable systems. We prove that the associated graded vector space of any filtered logarithmic vertex algebra has an induced structure of a non-local Poisson vertex algebra. We use this relation to obtain new examples of both logarithmic vertex algebras and non-local Poisson vertex algebras. Dedicated to Victor G. Kac on his 80th birthday.
The paper presents some results for reducing the computation of the Möbius functon of a Möbius category that arises from a combinatorial inverse semigroup to that of locally finite partially ordered sets. We illustrate the computation of the Möbius function with an example.