41 citations · 112 across the 23 of their papers we have counts for
26 papers
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…
Imaginary reflections and discrete symmetries in the heterotic Monster
Lisa Carbone, Natalie M. Paquette
Let be the Monster finite simple group. We give an interpretation of certain discrete symmetries of a family of heterotic string compactifications to dimension…
Entirety of certain cuspidal Eisenstein series on Kac--Moody groups
Lisa Carbone, Kyu-Hwan Lee, Dongwen Liu
Let be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on $…
On the convergence of Kac-Moody Eisenstein series
Lisa Carbone, Howard Garland, Kyu-Hwan Lee +2
Let be a representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We first consider Kac-Moody analogs of Borel Eisenstein…
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.
-systems of symmetrizable Kac-Moody algebras
Lisa Carbone, K. N. Raghavan, Biswajit Ransingh +2
As part of his classification of regular semisimple subalgebras of semisimple Lie algebras, Dynkin introduced the notion of a -system. This is a subset of the roots such that pa…
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…
Equivariant simplicial reconstruction
Lisa Carbone, Vidit Nanda, Yusra Naqvi
We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- ca…
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…
A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group
Lisa Carbone, Alex J. Feingold, Walter Freyn
Let A be a symmetrizable hyperbolic generalized Cartan matrix with Kac-Moody algebra g = g(A) and (adjoint) Kac-Moody group G = G(A)=$\langle\exp(ad(t e_i)), \exp(ad(t f_i)) \,|\,…
Kac--Moody groups and automorphic forms in low dimensional supergravity theories
Ling Bao, Lisa Carbone
Kac--Moody groups over have been conjectured to occur as symmetry groups of supergravity theories dimensionally reduced to dimensions less than 3, and their integr…
Uniqueness of representation--theoretic hyperbolic Kac--Moody groups over
Lisa Carbone, Frank Wagner
For a simply laced and hyperbolic Kac--Moody group over a commutative ring with 1, we consider a map from a finite presentation of obtained by Allcock and Carbo…
Root subsystems of rank 2 hyperbolic root systems
Lisa Carbone, Matt Kownacki, Scott H. Murray +1
Let be a rank 2 hyperbolic root system. Then has generalized Cartan matrix indexed by $a,b\in…
Presentation of hyperbolic Kac-Moody groups over rings
Daniel Allcock, Lisa Carbone
Tits has defined Kac-Moody and Steinberg groups over commutative rings, providing infinite dimensional analogues of the Chevalley-Demazure group schemes. Here we establish simple e…
Weyl group orbits on Kac--Moody root systems
Lisa Carbone, Alexander Conway, Walter Freyn +1
Let be a Dynkin diagram and let be the simple roots of the corresponding Kac--Moody root system. Let denote the Cartan suba…
Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
Lisa Carbone, Scott H. Murray, Hisham Sati
For a split, simply connected, semisimple Lie group of rank and the maximal compact subgroup of , we give a method for computing Iwasawa coordinates of $…
Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
Ling Bao, Lisa Carbone
Kac-Moody groups over have been conjectured to occur as symmetry groups of supergravities in dimensions less than 3, and their integer forms are co…
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…
Groups acting simply transitively on hyperbolic buildings
Lisa Carbone, Riikka Kangaslampi, Alina Vdovina
We construct and classify all groups, given by triangular presentations associated to the smallest thick generalized quadrangle, that act simply transitively on the vertices of hyp…
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…