Related papers: Constructing a Lie group analog for the Monster Li…
We consider several questions related to Pontryagin duality in the category of abelian pro-Lie groups.
We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
The fake monster Lie algebra is determined by the Borcherds function Phi_{12} which is the reflective modular form of the minimal possible weight with respect to O(II_{2,26}). We prove that the first non-zero Fourier-Jacobi coefficient of…
We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…
In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor)…
We adopt the $p$-group generation algorithm to classify small-dimensional nilpotent Lie algebras over small fields. Using an implementation of this algorithm, we list the nilpotent Lie algebras of dimension at most~9 over $\F_2$ and those…
We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.
We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When…
Let $\g$ be a complex orthogonal or symplectic Lie algebra and $\g'\subset \g$ the Lie subalgebra of rank $\rk \g'=\rk \g-1$ of the same type. We give an explicit construction of generators of the Mickelsson algebra $Z_q(\g,\g')$ in terms…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We give a complete classification of the class of Lie algebras of simply connected real Lie groups whose nontrivial coadjoint orbits are of codimension 1. Such a Lie group belongs to a well-known class, called the class of MD-groups. The…
The aim of this paper is to study a Lie conformal algebra of Block type. In this paper, conformal derivation, conformal module of rank 1 and low-dimensional comohology of the Lie conformal algebra of Block type are studied. Also, the vertex…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
In this work, we define the quasi-Poisson Lie quasigroups, dual objects to the quasi-poisson Lie groups and we establish the correspondance between the local quasi-Poisson Lie quasigroups and quasi-Lie bialgebras (up to isomorphism)
We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in Generalized Monstrous Moonshine, using a Borcherds-Kac-Moody Lie algebra decomposition due to…
We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.
It is shown that there is a $C^*$-algebraic quantum group related to any double Lie group. An algebra underlying this quantum group is an algebra of a differential groupoid naturally associated with a double Lie group
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra induces on it a non-trivial class of quadratic Poisson structures extending the linear Poisson bracket on the coadjoint orbits.
We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…