Related papers: The Poisson Geometry of Plancherel Formulas for Tr…
For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of…
Jacobi algebras, as the algebraic counterparts of Jacobi manifolds, are exactly the unital relative Poisson algebras. The direct approach of constructing Frobenius Jacobi algebras in terms of Manin triples is not available due to the…
We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of a compact Lie group. We show that all the faces of such an orbitope are exposed. The face structure is studied by means of the momentum map and it is shown that every…
Our goal is to find a representative of each orbit of the coadjoint action of the generalized Galile group on the dual of its Lie algebra. Our line of argument follows that of Cushman and van der Kallen, but differs in the details.
In this note, we give a description of the graded Lie algebra of double derivations of a path algebra as a graded version of the necklace Lie algebra equipped with the Kontsevich bracket. Furthermore, we formally introduce the notion of…
The purpose of this article is to analyze several Lie algebras associated to "orbit configuration spaces" obtained from a group G acting freely, and properly discontinuously on the upper 1/2-plane H^2. The Lie algebra obtained from the…
We define the periodic Full Kostant-Toda on every simple Lie algebra, and show its Liouville integrability. More precisely we show that this lattice is given by a Hamiltonian vector field, associated to a Poisson bracket which results from…
Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with…
The paper is devoted to the Poisson brackets compatible with multiplication in associative algebras. These brackets are shown to be quadratic and their relations with the classical Yang--Baxter equation are revealed. The paper also contains…
Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint…
In this paper, the notions of quasi-triangular and factorizable dual pre-Poisson bialgebras are introduced. A factorizable dual pre-Poisson bialgebra induces a factorization of the underlying dual pre-Poisson algebra, and the double of any…
The Geroch group is an infinite dimensional transitive group of symmetries of classical cylindrically symmetric gravitational waves which acts by non-canonical transformations on the phase space of these waves. Here this symmetry is…
Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing configuration using techniques of integrable systems. This allows…
We suggest two explicit descriptions of the Poisson q-W algebras which are Poisson algebras of regular functions on certain algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra g.…
In this paper we define a family of systems which have similarities with the Toda lattice. We construct two Lax pair representations and the associate Poisson structures for these systems. These systems lie between the classical Toda…
A non-linear map is applied onto the (non-standard) null-plane deformation of (3+1) Poincar\'e algebra giving rise to a simpler form of this triangular quantization. A universal $R$-matrix for the null plane quantum algebra is then obtained…
It is known that symmetric orbits in ${\bf g}^*$ for any simple Lie algebra ${\bf g}$ are equiped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the "canonical"…
In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real symmetric matrices) and the vector fields on the group of…
Kupavskii, Volostnov, and Yarovikov have recently shown that any set of $n$ points in general position in the plane has at least as many (partial) triangulations as the convex $n$-gon. We generalize this in two directions: we show that…
We prove that LG models for minimal semisimple adjoint orbits satisfy the Katzarkov-Kontsevich-Pantev conjecture about new Hodge theoretical invariants.