A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

A Portal Special Presentation- Geometric Unity: A First Look (edit)

No change in size , 25 April 2020

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 <p>[01:37:15] So I actually have a fair amount of freedom and I'm going to use a "magic bracket" notation, which in whatever situation I'm looking for, [the operator] knows what it wants to be, is does it. Want to do contraction? Does want to do wedge product, Lie product, Jordan product? But the point is, I now have a suite of ways of moving forms around.
-<p>[01:37:34] So, for example, I can define a Shiab ("Ship in a bottle") operator that takes [$$\Omega_{i}$$] $$i$$-forms valued in the adjoint bundle to much higher-degree forms valued in the adjoint bundle.
+<p>[01:37:34] So, for example, I can define a Shiab ("Ship in a bottle") operator that takes [$$\Omega^{i}$$] $$i$$-forms valued in the adjoint bundle to much higher-degree forms valued in the adjoint bundle.
 <p>[01:38:00] So, for in this case, for example [where i = 2], it would take a two-form to a d-minus-three-plus-two or a d-minus-one-form. So, curvature is an ad-valued two-form. And, if I had such a Shiab operator, it would take ad-valued two-forms to ad-valued d-minus-one-forms, which is exactly the right space to be an $$\alpha$$ coming from the derivative of an action.