41 citations · 112 across the 23 of their papers we have counts for
10 papers · 1 filter
Vertex operators for imaginary subalgebras in the Monster Lie Algebra
Darlayne Addabbo, Lisa Carbone, Elizabeth Jurisich +2
The Monster Lie algebra is a quotient of the physical space of the vertex algebra , where is the Moonshine module vertex ope…
Strong integrality of inversion subgroups of Kac-Moody groups
Abid Ali, Lisa Carbone, Dongwen Liu +1
Let be a symmetrizable generalized Cartan matrix with corresponding Kac--Moody algebra over . Let be an integrable highest weight -mod…
Constructing a Lie group analog for the Monster Lie algebra
Lisa Carbone, Elizabeth Jurisich, Scott H. Murray
We describe various approaches to constructing groups which may serve as Lie group analogs for the monster Lie algebra of Borcherds.
Generators and relations for (generalised) Cartan type superalgebras
Lisa Carbone, Martin Cederwall, Jakob Palmkvist
In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional L…
Commutator relations and structure constants for rank 2 Kac--Moody algebras
Lisa Carbone, Matt Kownacki, Scott H. Murray +1
We completely determine the structure constants between real root vectors in a rank 2 Kac--Moody algebra . Our description is computationally efficient, even in the r…
Infinite dimensional Chevalley groups and Kac-Moody groups over
Lisa Carbone, Dongwen Liu, Scott H. Murray
Let be a symmetrizable generalized Cartan matrix, which is not of finite or affine type. Let be the corresponding Kac-Moody algebra over a commutative ring w…
Generators and relations for Lie superalgebras of Cartan type
Lisa Carbone, Martin Cederwall, Jakob Palmkvist
We give an analog of a Chevalley-Serre presentation for the Lie superalgebras W(n) and S(n) of Cartan type. These are part of a wider class of Lie superalgebras, the so-called tens…
Dimensions of Imaginary Root Spaces of Hyperbolic Kac--Moody Algebras
Lisa Carbone, Walter Freyn, Kyu-Hwan Lee
We discuss the known results and methods for determining root multiplicities for hyperbolic Kac--Moody algebras.
Eisenstein series on rank 2 hyperbolic Kac--Moody groups
Lisa Carbone, Kyu-Hwan Lee, Dongwen Liu
We define Eisenstein series on rank 2 hyperbolic Kac--Moody groups over R, induced from quasi--characters. We prove convergence of the constant term and hence the almost everywhere…
Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
Lisa Carbone, Sjuvon Chung, Leigh Cobbs +4
We give a criterion for a Dynkin diagram, equivalently a generalized Cartan matrix, to be symmetrizable. This criterion is easily checked on the Dynkin diagram. We obtain a simple…