Related papers: Gelfand-Dikii Brackets for Nonstandard Lax Equatio…
Starting from Borcherds' fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose…
We construct free Lie algebras which, together with the algebra of spatial rotations, form infinite-dimensional extensions of finite-dimensional Galilei Maxwell algebras appearing as global spacetime symmetries of extended non-relativistic…
A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed employing the dressing method and deformed vertex operators which takes into account the…
We present two non-equivalent families of hierarchies of non-Abelian compatible maps and we provide their Lax pair formulation. These maps are associated with families of hierarchies of non-Abelian Yang-Baxter maps, which we provide…
We determine the Lie subalgebra $\mathfrak{g}_{nil}$ of a Borcherds symmetrizable generalized Kac-Moody Lie algebra $\mathfrak{g}$ generated by $ad$-locally nilpotent elements and show that it is `essentially' the same as the Levi…
In this paper we extend several results about root systems of Kac-Moody algebras to superalgebra context. In particular, we describe the root bases and the sets of imaginary roots.
A combinatorial construction of a Gelafand model for the symmetric group and its Iwahori-Hecke algebra is presented.
We consider Laplace transforms of the Picard-Fuchs differential equations of Calabi-Yau hypersurfaces and calculate their Stokes matrices. We also introduce two different types of Laplace transforms of Gel'fand-Kapranov-Zelevinski…
We propose a new construction of Banach-Lie groups and algebras relying on nonstandard analysis. A major standard application is the Local Theorem which to certain extent reduces the problem of associating a Lie group to a given banach-Lie…
Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite…
In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $T$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length…
Lie n-algebroids and Lie infinity algebroids are usually thought of exclusively in supergeometric or algebraic terms. In this work, we apply the higher derived brackets construction to obtain a geometric description of Lie n-algebroids by…
In this paper we extend to the abstract A-framework some existence theorems for differential inclusion problems with Dirichlet boundary conditions.
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
The Weil algebra of a semisimple Lie group and an exterior algebra of a symplectic manifold possess antibrackets. They are applied to formulate the models of non--abelian equivariant cohomologies.
We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section…
A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known…
We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms…
Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each…
This work is devoted to the algebraic and arithmetic properties of Rankin-Cohen brackets allowing to define and study them in several natural situations of number theory. It focuses on the property of these brackets to be formal…