http://dspace.nbuv.gov.ua:80/handle/123456789/146007 2026-04-17T05:57:25Z 2026-04-17T05:57:25Z Girelli, F. http://dspace.nbuv.gov.ua:80/handle/123456789/146535 2019-02-09T23:24:55Z 2010-01-01T00:00:00Z

Snyder Space-Time: K-Loop and Lie Triple System Girelli, F. Different deformations of the Poincaré symmetries have been identified for various non-commutative spaces (e.g. κ-Minkowski, sl(2,R), Moyal). We present here the deformation of the Poincaré symmetries related to Snyder space-time. The notions of smooth ''K-loop'', a non-associative generalization of Abelian Lie groups, and its infinitesimal counterpart given by the Lie triple system are the key objects in the construction.

2010-01-01T00:00:00Z Piacitelli, G. http://dspace.nbuv.gov.ua:80/handle/123456789/146534 2019-02-09T23:24:54Z 2010-01-01T00:00:00Z

Quantum Spacetime: a Disambiguation Piacitelli, G. We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the ''canonical quantum spacetime''. The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance.

2010-01-01T00:00:00Z Hasebe, K. http://dspace.nbuv.gov.ua:80/handle/123456789/146533 2019-02-09T23:24:57Z 2010-01-01T00:00:00Z

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres Hasebe, K. This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an interesting hierarchical structure made of ''compounds'' of lower dimensional spheres. We give a physical interpretation for such particular structure of fuzzy spheres by utilizing Landau models in generic even dimensions. With Grassmann algebra, we also introduce a graded version of the Hopf map, and discuss its relation to fuzzy supersphere in context of supersymmetric Landau model.

2010-01-01T00:00:00Z Asakawa, T. Watamura, S. http://dspace.nbuv.gov.ua:80/handle/123456789/146532 2019-02-09T23:24:32Z 2010-01-01T00:00:00Z

Twist Quantization of String and Hopf Algebraic Symmetry Asakawa, T.; Watamura, S. We describe the twist quantization of string worldsheet theory, which unifies the description of quantization and the target space symmetry, based on the twisting of Hopf and module algebras. We formulate a method of decomposing a twist into successive twists to analyze the twisted Hopf and module algebra structure, and apply it to several examples, including finite twisted diffeomorphism and extra treatment for zero modes.

2010-01-01T00:00:00Z