Extensions essentielles d'algèbres de Lie classiques de dimensions infinies
(Finite) presentations of the Albert-Frank-Shalev Lie algebras
In questo lavoro vengono studiate le algebre di Albert-Frank-Shalev. Queste sono algebre di Lie modulari di dimensione infinita, ottenute da un loop di certe algebre semplici di dimensione finita. Si dimostra che le algebre di Albert-Frank-Shalev sono unicamente determinate, a meno di elementi centrali o secondo centrali, da un certo quoziente finito-dimensionale. Tale risultato si ottiene dando la presentazione finita di un'algebra il cui quoziente sul secondo centro (infinito-dimensionale) è isomorfo...
Free field approach to solutions of the quantum Knizhnik-Zamolodchikov equations.
Generalized Kac-Moody algebras and the modular function j.
Generalized Verma modules, loop space cohomology and MacDonald-type identities
Graded Lie algebras of maximal class IV
Groups of strings.
Heisenberg algebra and a graphical calculus
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of the vector spaces of morphisms between products of generating objects in this category.
Holomorphic automorphisms and collective compactness in J*-algebras of operator
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball in a J*-algebra of operators. Let be the family of all collectively compact subsets W contained in . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when is a Cartan factor.
Hyperbolic Lie Algebras and Quasi-Regular Cusps on Hilbert Modular Surfaces.
Induced modules for affine Lie algebras.
Infinite dimensional Lie algebras: representations and applications
Infinite Root Systems, Representations of Graphs and Invariant Theory.
Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits
In this paper, we construct a hyperkähler structure on the complexification of any Hermitian symmetric affine coadjoint orbit of a semi-simple -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of . By a relevant identification of the complex orbit with the cotangent space of induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on compatible with...
Infinite-dimensional Lie groups and algebras in mathematical physics.
Invariant cohomology of the Poisson Lie algebra of a symplectic manifold
Invariant theory and the algebra with negative integral central charge
The vertex algebra with central charge may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer , it was conjectured in the physics literature that should have a minimal strong generating set consisting of elements. Using a free field realization of due to Kac–Radul, together with a deformed version of Weyl’s first and second fundamental theorems of invariant theory for the standard representation of ,...
Invariant Theory for Generalized Root Systems.
Isomorphisms of Lie algebras of vector fields
Kac-Moody algebras: An introduction for physicists