Related papers: Poisson Poincare groups

Poisson transversals are those submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In a previous note we proved a normal form theorem around such submanifolds. In this communication, we…

Admissible point transformations of classes of $r$th order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first…

We describe infinitesimally Dirac groupoids via geometric objects that we call Dirac bialgebroids. In the two well-understood special cases of Poisson and presymplectic groupoids, the Dirac bialgebroids are equivalent to the Lie…

We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.

In this article we construct a large family of $R$-matrices for various extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice and admit $R$-matrices in…

A natural family of quantized matrix algebras is introduced. It includes the two best studied such. Located inside ${\s U}_q(A_{2n-1})$, it consists of quadratic algebras with the same Hilbert series as polynomials in $n^2$ variables. We…

We recall the construction of non-formal deformation quantization of the Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.

In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.

We obtain the Poincare group generators by proper choice of arbitrary functions present in the Relativistic Theory of Gravitation (RTG) Hamiltonian. Their Dirac brackets give the Poincare algebra in accordance with the fact that RTG has 10…

It is well known that many famous Burnside-type problems have positive solutions for PI-groups and PI-algebras. In the present article we also consider various Burnside-type problems for PI-groups and PI-representations of groups.

Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix…

We use braided groups to introduce a theory of $*$-structures on general inhomogeneous quantum groups, which we formulate as {\em quasi-$*$} Hopf algebras. This allows the construction of the tensor product of unitary representations up to…

We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…

We give the canonical normal form for the elements of the finite or infinite alternating groups using local stationary presentation of these groups.

Poincar\'e and Eisenstein series are building blocks for every type of modular forms. We define Poincar\'e series for Jacobi forms of lattice index and state some of their basic properties. We compute the Fourier expansions of Poincar\'e…

Explicit formulas for computation of the Poincar\'e series for the algebras of joint $SL_2$-invariants and covariants of $n$ linear forms in terms of Narayana polynomials are found. Also, for these algebras we calculate the degrees and…

Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…

We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.

We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.

Let W be a Coxeter group. We show that a certain power series involving a sum over all involutions in W can be expressed in terms of the Poincare series of W. (The case where W is finite is already known,)