Some Infinite-Dimensional Algebras Arising in Spin Systems and in Particle Physics and their Grand Algebra |
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| Authors: | Aaraki Huzihiro Flato Moshé Michéa Sébastien Sternheimer Daniel |
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| Institution: | (1) Department of Mathematics, Faculty of Science and Technology, Science and Technology, Science University of Tokyo, Yamazaki 2641, Noda-shi, c[Chiba-ken, 278, Japan. e-mail;(2) Département de Mathématiques, Université de Bourgogne, Laboratoire Gevrey de Mathématique Physique, CNRS ESA 5029, BP 400, F-21011 Dijon Cedex, France e-mail |
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| Abstract: | We indicate similarities in the structure of two types of infinite-dimensional algebras, one introduced 28 years ago in connection with the mass problem of elementary particles and the other seven years ago in connection with spin systems (XY models). We show that these algebras can be considered as representations of a single  Grand Algebra , the enveloping algebra of an affine Kac–Moody algebra built on the Poincaré Lie algebra. As an associative and coassociative bialgebra of operators, the latter representation of the grand algebra is a preferred nontrivial deformation of the Ising case bialgebra. |
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| Keywords: | infinite-dimensional algebras deformations grand algebra elementary particle symmetries spin systems |
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