On PBW-deformations of braided exterior algebras

TL;DR

This paper classifies PBW-deformations of certain quantum exterior algebras related to fundamental modules of quantum rak{sl}_N, finding unique deformations in some cases and none in others, with comparisons to quantum Clifford algebras.

Contribution

It provides a classification of PBW-deformations for specific quantum exterior algebras and identifies cases with unique or no deformations, enriching the understanding of quantum algebra structures.

Findings

First two cases do not admit deformations

Third case yields a unique algebra with good properties

Comparison with quantum Clifford algebras in literature

Abstract

We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that the first two cases do not admit any deformation, while in the third case we obtain an essentially unique algebra with good properties. We compare this algebra with other quantum Clifford algebras appearing in the literature.