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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 19th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexam giving this its own little entry (in line with [[Spin(2)]], [[Spin(3)]], [[Spin(4)]], [[Spin(5)]]). For the moment just as to record a nice reference for the exceptional iso $Spin(6) \simeq SU(4)$ <a href="https://ncatlab.org/nlab/revision/Spin%286%29/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Spin%286%29">current</a>

   am giving this its own little entry (in line with Spin(2), Spin(3), Spin(4), Spin(5)). For the moment just as to record a nice reference for the exceptional iso $Spin(6) \simeq SU(4)$

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 29th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added the picture of Dynkin diagrams that illustrates the exceptional iso $Spin(6) \simeq SU(4)$ ([here](https://ncatlab.org/nlab/show/Spin(6)#IsomorphismBetweenSpin6AndSU4)). Am adding this also at _[[SU(4)]]_ and at _[[A3]]_ <a href="https://ncatlab.org/nlab/revision/diff/Spin%286%29/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/Spin%286%29/9">v9</a>, <a href="https://ncatlab.org/nlab/show/Spin%286%29">current</a>

   I have added the picture of Dynkin diagrams that illustrates the exceptional iso $Spin(6) \simeq SU(4)$ (here). Am adding this also at SU(4) and at A3

   diff, v9, current

3. • CommentRowNumber3.
   • CommentAuthorJohn Baez
   • CommentTimeJan 15th 2021
   • PermaLink
   Author: John Baez
   Format: MarkdownItexI added another explanation of why Spin(6) is SU(4). I should do the same sort of thing for Spin(5) and Spin(4). <a href="https://ncatlab.org/nlab/revision/diff/Spin%286%29/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/Spin%286%29/11">v11</a>, <a href="https://ncatlab.org/nlab/show/Spin%286%29">current</a>

   I added another explanation of why Spin(6) is SU(4).

   I should do the same sort of thing for Spin(5) and Spin(4).

   diff, v11, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 16th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have hyperlinked more of the technical terms (such as _[[Hodge star operator]]_) and also made explicit some more technical terms used in the formulas (such as _[[dual vector space]]_) <a href="https://ncatlab.org/nlab/revision/diff/Spin%286%29/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/Spin%286%29/14">v14</a>, <a href="https://ncatlab.org/nlab/show/Spin%286%29">current</a>

   I have hyperlinked more of the technical terms (such as Hodge star operator) and also made explicit some more technical terms used in the formulas (such as dual vector space)

   diff, v14, current