Lattice vertex algebras and combinatorial bases: general case and W-algebras
نویسندگان
چکیده
We introduce what we call the principal subalgebra of a lattice vertex (super) algebra associated to an arbitrary Z-basis of the lattice. In the first part (to appear), the second author considered the case of positive bases and found a description of the principal subalgebra in terms of generators and relations. Here, in the most general case, we obtain a combinatorial basis of the principal subalgebra WL and of related modules. In particular, we substantially generalize several results in Georgiev, 1996, covering the case of the root lattice of type An, as well as some results from Calinescu, Lepowsky and Milas, 2010. We also discuss principal subalgebras inside certain extensions of affine W-algebras coming from multiples of the root lattice of type An.
منابع مشابه
Weighted Convolution Measure Algebras Characterized by Convolution Algebras
The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.
متن کاملVertex Representations via Finite Groups and the Mckay Correspondence
where the first factor is a symmetric algebra and the second one is a group algebra. The affine algebra ĝ contains a Heisenberg algebra ĥ. One can define the so-called vertex operators X(α, z) associated to α ∈ Q acting on V essentially using the Heisenberg algebra ĥ. The representation of ĝ on V is then obtained from the action of the Heisenberg algebra ĥ and the vertex operators X(α, z) assoc...
متن کاملFull Heaps and Representations of Affine Kac–moody Algebras
We give a combinatorial construction, not involving a presentation, of almost all untwisted affine Kac–Moody algebras modulo their onedimensional centres in terms of signed raising and lowering operators on a certain distributive lattice B. The lattice B is constructed combinatorially as a set of ideals of a “full heap” over the Dynkin diagram, which leads to a kind of categorification of the p...
متن کاملLattice of full soft Lie algebra
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a ...
متن کاملA classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
متن کامل