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A Deformed Quon Algebra

Hery Randriamaro (2019)

Communications in Mathematics

The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators a i , k , ( i , k ) * × [ m ] , on an infinite dimensional vector space satisfying the...

A minimal Set of Generators for the Ring of multisymmetric Functions

David Rydh (2007)

Annales de l’institut Fourier

The purpose of this article is to give, for any (commutative) ring A , an explicit minimal set of generators for the ring of multisymmetric functions T S A d ( A [ x 1 , , x r ] ) = A [ x 1 , , x r ] A d 𝔖 d as an A -algebra. In characteristic zero, i.e. when A is a -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...

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