In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing approach observables form a quotient Dirac bracket algebra. We show that these two algebras are isomorphic. A new realization of the observable algebras through the original Poisson bracket is found.Generators, brackets and pointwise products of ...

We prove that if X is a locally compact σ-compact space then on its quotient, γ(X) say, determined by the algebra of all real valued bounded continuous functions on X, the quotient topology and the completely regular topology defined by this algebra are equal. It follows from this that if X is second countable locally compact then γ(X) is second countable locally compact Hausdorff if and only i...

The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1skeleton of the ...

We comment on the conformal boundary states of the c = 1 free boson theory on a circle which do not preserve the U(1) symmetry. We construct these Virasoro boundary states at a generic radius by a simple asymmetric shift orbifold acting on the fundamental boundary states at the self-dual radius. We further calculate the boundary entropy and find that the Virasoro boundary states at irrational r...

We prove the following result concerning the inheritance of hyper-duality by block and quotient Bose-Mesner algebras associated with a hyper-dual pair of imprimitive Bose-Mesner algebras. Let M and M̃ denote Bose-Mesner algebras. Suppose there is a hyper-duality ψ from the subconstituent algebra of M with respect to p to the subconstituent algebra of M̃ with respect to p̃. Also suppose thatM is im...

Let W be a Coxeter group with Coxeter graph Γ. Let H be theassociated Hecke algebra. We define a certain ideal I in H and study thequotient algebra H̄ = H/I. We show that when Γ is one of the infinite seriesof graphs of type E, the quotient is semi-simple. We examine the cell structuresof these algebras and construct their irreducible representations. We discussthe case where...

Let R be a non empty poset and let A, B be many sorted sets indexed by R. One can check that every many sorted relation between A and B which is os-compatible is also order-sorted. Let R be a non empty poset and let A be a many sorted set indexed by the carrier of R. An order sorted relation of A is an order sorted relation of A, A. Let S be an order sorted signature and let U1 be an order sort...

The articles [16], [9], [19], [18], [13], [1], [6], [21], [5], [10], [12], [17], [20], [7], [8], [15], [11], [2], [3], and [4] provide the notation and terminology for this paper. We consider structures of the type algebra as extensions of 1-sorted structure as systems 〈 a carrier, a left quotient, a right quotient, an inner product 〉, where the carrier is a set and the left quotient, the right...