New realizations of observables in dynamical systems with second class constraints. Abstract In the Dirac bracket approach to dynamical systems with second class constrains the observables are represented by elements of a quotient Dirac bracket algebra. We describe the constraints which allow to construct families of new realizations of this algebra. The realizations are obtained as quotients o...

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

New realizations of observables in dynamical systems with second class constraints. Abstract In the Dirac bracket approach to dynamical systems with second class constrains the observables are represented by elements of a quotient Dirac bracket algebra. We describe the constraints which allow to construct families of new realizations of this algebra. The realizations are obtained as quotients o...

Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with grU = A is Koszul dual to a differential graded algebra (A!, d). We relate the module categories of this dual pair by a⊗−Hom adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg, and Soergel.

Two types of congruences are introduced in a distributive lattice, one in terms of ideals generated by derivations and the other in terms of images of derivations. An equivalent condition is derived for the corresponding quotient algebra to become a Boolean algebra. An equivalent condition is obtained for the existence of a derivation. 2000 Mathematics Subject Classification: 06D99, 06D15.

Representations of the twisted Heisenberg-Virasoro algebra at level zero. Abstract. We describe the structure of the irreducible highest weight modules for the twisted Heisenberg-Virasoro Lie algebra at level zero. We prove that such a module is either isomorphic to a Verma module or to a quotient of two Verma modules.

In this paper, we define a Hopf algebra structure on the vector space spanned by packed words using a selection-quotient coproduct. We show that this algebra is free on its irreducible packed words. Finally, we give some brief explanations on the Maple codes we have used.

Let K be a compact Lie group. We compute the abelianization of the Lie algebra of equivariant vector fields on a smooth K-manifold X . We also compute the abelianization of the Lie algebra of strata preserving smooth vector fields on the quotient X/K.

In the theory of algebraic group actions on affine varieties, the concept of a Kempf–Ness set is used to replace the geometric quotient by the quotient with respect to a maximal compact subgroup. By making use of the recent achievements of “toric topology” we show that an appropriate notion of a Kempf–Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate su...

We introduce a certain cellular algebra Q(n; r) which is a quotient of the q-Schur algebra S q (n; r). This is naturally equipped with a canonical basis which is compatible with Lusztig's canonical bases for certain modules for the quantized enveloping algebra U (sl n). We describe a diagram calculus for Q(n; r) which makes calculations involving the corresponding canonical bases easy to unders...