TL;DR
This paper reformulates para-statistics using Lie-super triple systems, reproduces recent discoveries of new para-statistics, and explores non-commuting bosonic and fermionic operators.
Contribution
It introduces a Lie-super triple system framework for para-statistics, extending the understanding of their algebraic structure and relationships.
Findings
Reproduces recent new para-statistics using Lie-super triple systems
Shows bosonic and fermionic operators may not commute
Provides a unified algebraic framework for para-statistics
Abstract
We first reformulate para-statistics in terms of Lie-super triple systems. In this way, we reproduce various new kinds of para-statistics discovered recently by Palev in addition to the standard one. Also, bosonic and fermionic operators may not necessarily commute with each other.
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