Related papers: Full universal enveloping vertex algebras from fac…
Background: The vacuum in the light-front representation of quantum field theory is trivial while vacuum in the equivalent canonical representation of the same theory is non-trivial. Purpose: Understand the relation between the vacuum in…
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly…
A. L. Agore and G. Militaru constructed a new invariant (a ``universal coacting Hopf algebra") for some finite-dimensional binary quadratic algebras such as Lie/Leibniz algebras, associative algebras, and Poisson algebras with prominent…
Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic…
We construct homomorphisms from the universal enveloping algebra of the positive (part of the) Witt algebra to several different Artin-Schelter regular algebras, and determine their kernels and images. As a result, we produce elementary…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
Let $k$ be an arbitrary field, $\Lambda$ be a $k$-algebra and $V$ be a $\Lambda$-module. When it exists, the universal deformation ring $R(\Lambda,V)$ of $V$ is a $k$-algebra whose local homomorphisms to $R$ parametrize the lifts of $V$ up…
In this paper we give a construction of the universal enveloping algebra of a Malcev algebra in categories of group algebra comodules with a symmetry given by a bicharacter of the group. A particular example of such categories is the…
We examine generalized global symmetries as a kind of compactly supported cohomology, and so are led to revisit questions about the locality of quantum field theory, following Segal. Physics naturally suggests a generalization of…
A lot of developments made during the last years show that Kac-Moody algebras play an important role in the algebraic structure of some supergravity theories. These algebras would generate infinite-dimensional symmetry groups. The possible…
We develop a theory of $\phi$-coordinated (quasi) modules for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their $\phi$-coordinated (quasi) modules, where $\phi$ is what we call an…
Galilean $W_3$ vertex operator algebra $\mathcal GW_3(c_L,c_M)$ is constructed as a universal enveloping vertex algebra of certain non-linear Lie conformal algebra. It is proved that this algebra is simple by using determinant formula of…
Given a finite-dimensional reductive Lie algebra $\mathfrak{g}$ equipped with a nondegenerate, invariant, symmetric bilinear form $B$, let $V^k(\mathfrak{g},B)$ denote the universal affine vertex algebra associated to $\mathfrak{g}$ and $B$…
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
Gauged linear sigma-models at critical coupling on Riemann surfaces yield self-dual field theories, their classical vacua being described by the vortex equations. For local models with structure group ${\rm U}(r)$, we give a description of…
We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…
Universal Deformation Formulas (UDFs) for the deformation of associative algebras play a key role in deformation quantization. Here we present examples for certain classes of infinitesimals. A basic representable 2-cocycle $F$ of an…
A vertex-algebraic analogue of the Lie algebroid complex is constructed, which generalizes the "small" chiral de Rham complex on smooth manifolds. The notion of VSA-inductive sheaves is also introduced. This notion generalizes that of…
We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.