Related papers: Tree Algebras: An algebraic axiomatization of inte…

We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations…

Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex algebra and its representation category become a bundle over…

We establish rigid tensor category structure on finitely-generated weight modules for the subregular $W$-algebras of $\mathfrak{sl}_n$ at levels $ - n + \frac{n}{n+1}$ (the $\mathcal{B}_{n+1}$-algebras of Creutzig-Ridout-Wood) and at levels…

An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…

We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex. We also give a characterization for the algebras whose trivial extensions are Brauer line/star/cycle algebras. As a…

In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain quivers, and torus orbits on certain homogeneous varieties. In…

We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2-cofiniteness. We also showed that the tensor product theory develops…

A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce two nilpotent Lie algebras and their extended solvable Lie…

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…

In this paper we build an abstract description of vertex algebras from their basic axioms. Starting with Borcherds' notion of a vertex group, we naturally construct a family of multilinear singular maps parameterised by trees. These…

Vertex algebras can be defined over any differential commutative ring. We develop the general descent theory for vertex algebras over such bases. We apply this to the classification of twisted forms of affine and Heisenberg vertex algebras,…

The notion of a Z-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethories can also be considered non-linear generalizations of…

We construct a family of vertex algebras associated to the current algebra of finite-dimensional abelian Lie algebras along with their modules and logarithmic modules. We show this family of vertex algebras and their modules are…

The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…

Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\tau_i:X \to X$ for $1 \le i \le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra…

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

For a finite-dimensional simple Lie algebra $\mathfrak{g}$, we use the vertex tensor category theory of Huang and Lepowsky to identify the category of standard modules for the affine Lie algebra $\hat{\mathfrak{g}}$ at a fixed level…