GL_q(N)-covariant braided differential bialgebras

TL;DR

This paper explores the construction of braided differential bialgebras and Hopf algebras covariant under GL_q(N), including their applications to quantum hyperplanes and the braided matrix algebra, with implications for quantum spacetime symmetries.

Contribution

It introduces the concept of differential bialgebras on quantum spaces, extending the structure to include both additive and multiplicative coproducts, and relates these to quantum spacetime models.

Findings

Established differential bialgebras on quantum hyperplanes.

Constructed braided matrix algebra with dual coproducts.

Connected the algebraic structures to q-Minkowski space and q-Poincare algebra.

Abstract

We study a possibility to define the (braided) comultiplication for the GLq(N)-covariant differential complexes on some quantum spaces. We discover such `differential bialgebras' (and Hopf algebras) on the bosonic and fermionic quantum hyperplanes (with additive coproduct) and on the braided matrix algebra BMq(N) with both multiplicative and additive coproducts. The latter case is related (for N=2) to the q-Minkowski space and q-Poincare algebra.