http://dspace.nbuv.gov.ua:80/handle/123456789/146039 Thu, 16 Apr 2026 11:24:45 GMT 2026-04-16T11:24:45Z http://dspace.nbuv.gov.ua:80/bitstream/id/435083/ http://dspace.nbuv.gov.ua:80/handle/123456789/146039 http://dspace.nbuv.gov.ua:80/handle/123456789/148553 The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions Johnson-Freyd, T. We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|4//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively.; We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|⁴//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/148553 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/148551 Un-Reduction of Systems of Second-Order Ordinary Differential Equations García-Toraño Andrés, E.; Mestdag, T. In this paper we consider an alternative approach to ''un-reduction''. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) ''primary un-reduced SODE'', and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/148551 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/148549 Cartan Connections on Lie Groupoids and their Integrability Blaom, A.D. A multiplicatively closed, horizontal n-plane field D on a Lie groupoid G over M generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection D is a Cartan connection ∇ on the Lie algebroid of G, a notion already studied elsewhere by the author. It is shown that ∇ may be regarded as infinitesimal parallel translation in the groupoid G along D. From this follows a proof that D defines a pseudoaction generating a pseudogroup of transformations on M precisely when the curvature of ∇ vanishes. A byproduct of this analysis is a detailed description of multiplication in the groupoid J¹G of one-jets of bisections of G. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/148549 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/148548 On Free Field Realizations of W(2,2)-Modules Adamović, D.; Radobolja, G. The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra H at level zero as modules for the W(2,2)-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322-4342, arXiv:1405.1707]. We prove that the irreducible highest weight H-module is irreducible as W(2,2)-module if and only if it has a typical highest weight. Finally, we construct a screening operator acting on the Heisenberg-Virasoro vertex algebra whose kernel is exactly W(2,2) vertex algebra. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/148548 2016-01-01T00:00:00Z