Lie Algebras and Braided Geometry

Abstract

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view about $q$-Minkowski space which arises in a similar way as the enveloping algebra of the braided Lie algebra $g{l}_{2,q}$. Our point of view fixes the signature of the metric on $q$-Minkowski space and hence also of ordinary Minkowski space at $q=1$. We also describe an abstract construction for left-invariant integration on any braided group.

19 pages (corrected title)

References in corpus (3)

• Braided Momentum Structure of the q-Poincare Group
• Quantum and Braided Linear Algebra
• On the Addition of Quantum Matrices

Cited by in corpus (4)

• Introduction to Braided Geometry and $q$-Minkowski Space
• Braided Matrix Structure of $q$-Minkowski Space and $q$-Poincare Group
• Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups
• Further results on coset representative categories