Lie Algebras and Braided Geometry

Details Lie Algebras and Braided Geometry Lie Algebras and Braided Geometry

1993-11-18

arxiv.org/abs/hep-th/9311109v3

Physics

High Energy Physics

High Energy Physics - Theory

19 pages (corrected title)

Scientific paper

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 $gl_{2,q}$. 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.

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