Homogeneous algebras, statistics and combinatorics

Simple item page
dc.creatorDubois-Violette, Michel
dc.creatorPopov, Todor
dc.date2002-07-10
dc.date2002-09-10
dc.date.accessioned2026-07-07T04:49:37Z
dc.date.available2026-07-07T04:49:37Z
dc.descriptionAfter some generalities on homogeneous algebras, we give a formula connecting the Poincaré series of a homogeneous algebra with the homology of the corresponding Koszul complex generalizing thereby a standard result for quadratic algebras. We then investigate two particular types of cubic algebras: The first one called the parafermionic (parabosonic) algebra is the algebra generated by the creation operators of the universal fermionic (bosonic) parastatics with $D$ degrees of freedom while the second is the plactic algebra that is the algebra of the plactic monoid with entries in $\{1,2,..., D\}$. In the case D=2 we describe the relations with the cubic Artin-Schelter algebras. It is pointed out that the natural action of GL(2) on the parafermionic algebra for D=2 extends as an action of the quantum group $GL_{p,q}(2)$ on the generic cubic Artin-Schelter regular algebra of type $S_1$; $p$ and $q$ being related to the Artin-Schelter parameters. It is claimed that this has a counterpart for any integer $D\geq 2$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0207085
dc.identifierhttp://arxiv.org/abs/math/0207085
dc.identifierLett.Math.Phys. 61 (2002) 159-170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64488
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleHomogeneous algebras, statistics and combinatorics
dc.typetext

Files

Collections

arXiv