Some infinite-dimensional algebras arising in spin systems and in particle physics and their grand algebra (Q1386537)

The paper presents some similarities in the structure of two types of infinite-dimensional algebras: the first one arising from affine semisimple groups and connected with the mass problem of elementary particles, and the second one introduced quite recently in connection with spin systems (\(XY\)-model). The authors show that these two algebras can be considered as representations of a bigger ``grand algebra'', which is the enveloping algebra of an affine Kac-Moody algebra built on the Poincaré Lie algebra.