Paragrassmann Analysis and Quantum Groups

TL;DR

This paper explores the algebraic structure of paragrassmann algebras and their connection to quantum groups, introducing derivatives and covariant derivatives to extend Grassmann calculus.

Contribution

It provides a new algebraic approach to paragrassmann algebras and establishes deep links with quantum groups at roots of unity, without relying on the Green ansatz.

Findings

Defined differentiation operators for paragrassmann variables

Introduced covariant para-super-derivatives extending Grassmann calculus

Established relations between paragrassmann algebras and quantum groups at roots of unity

Abstract

Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. Operators of differentiation with respect to paragrassmann variables and a covariant para-super-derivative are introduced giving a natural generalization of the Grassmann calculus to a paragrassmann one. Deep relations between paragrassmann algebras and quantum groups with deformation parameters being roots of unity are established.