Year: 2026
Type: article
Abstract: In this paper we reexamine the definition of parafermions and parabosons by means of Green’s triple relations, and extend these relations by including a parity operator P which is also determined by means of triple relations. As a consequence, we are dealing with new algebraic structures. It is shown that the algebra underlying a set of n parafermions together with P is the orthogonal Lie algebra so ( 2 n + 2 ) . The Fock spaces correspond to particular irreducible representations of so ( 2 n + 2 ) , and the action of P in these spaces leads to interesting observations. Next, we show that the algebra underlying a set of n parabosons together with P is the orthosymplectic Lie superalgebra osp ( 2 | 2 n ) . In this case, the Fock spaces correspond to certain irreducible infinite-dimensional representations of osp ( 2 | 2 n ) . Both for parafermions and parabosons the spectrum of P is closely related to the so-called order of statistics p , introduced by Green.
Authors: N I Stoilova, J Van der Jeugt
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Bulgarian National Science Fund
Award: G3602433328
OpenAlex ID: W7154147785
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