If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 → C(K) → Y → X → 0, where K = [0, 1] or ωω . For the case K = [0, 1] we show that there exists a twisted sum whose quotient map is strictly singular if and only if X contains no copy of `1. If K = ωω we prove an analogue of a theorem of Johnson and Zippin (for K = [0, 1]) by showing that all such twisted s...

Let M be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group G. Let M//G = φ(0)/G = M0 be the symplectic quotient at value 0 of the moment map φ. The space M0 may in general not be smooth. It is known that, as vector spaces, there is a natural isomorphism between the quantum Hilbert space over M0 and the G-invariant subspace of the...

This set of lectures contain a brief review of some basic supersymmetry and its representations , with emphasis on superspace and superfields. Starting from the Poincaré group, the supersymmetric extensions allowed by the Coleman-Mandula theorem and its generalisation to superalgebras, the Haag, Lopuszanski and Sohnius theorem, are discussed. Minkowski space is introduced as a quotient space an...

We apply the saturation heuristic to the bisimulation problem for deterministic discrete-event models, obtaining the fastest to date symbolic bisimulation algorithm, able to deal with large quotient spaces. We compare performance of our algorithm with that of Wimmer et al., on a collection of models. As the number of equivalence classes increases, our algorithm tends to have improved time and s...

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail. 0. Introduction A homogeneous space X of a Lie group G may be always identified wit...

We show that the symmetric product of a flat affine scheme over a commutative ring can be embedded into the quotient by the general linear group of the scheme of commuting matrices. We also prove that the symmetric product of the affine space is isomorphic to the above quotient when the base ring is a characteristic zero field. Over an infinite field of arbitrary characteristic the quotient of ...

This set of lectures contain a brief review of some basic supersymmetry and its representations , with emphasis on superspace and superfields. Starting from the Poincaré group, the supersymmetric extensions allowed by the Coleman-Mandula theorem and its generalisation to superalgebras, the Haag, Lopuszanski and Sohnius theorem, are discussed. Minkowski space is introduced as a quotient space an...

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If A is a reflexive, amenable Banach algebra such that for each maximal left ideal L of A (i) the quotient A/L has t...