*-Structures on Braided Spaces

TL;DR

This paper investigates $*$-structures on quantum and braided spaces defined by R-matrices, focusing on duality and applications in braided geometry, including $q$-Minkowski and $q$-Euclidean spaces.

Contribution

It establishes the duality between $*$-braided groups of vectors and covectors and explores initial applications in braided geometry.

Findings

Duality between vector and covector $*$-braided groups proved.

$*$-structures on $q$-Minkowski and $q$-Euclidean spaces analyzed.

Foundations for applications in braided geometry laid out.

Abstract

$*$-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include $q$-Minkowski and $q$-Euclidean spaces as additive braided groups. The duality between the $*$-braided groups of vectors and covectors is proved and some first applications to braided geometry are made.