Experimental: LinearAlgebraicGroups
#5665
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Nice to see such things in Oscar. Just a quick question (out of curiosity): What is the definition of "linear algebraic groups" that these objects here correspond to? |
A linear algebraic group is an affine variety with a group strucutre. These groups can be embedded into a GL_n and here we (at the moment) only focus on that and not on the variety itself. |
| * [My Name](https://my-webpage.com/) | ||
| * [Other Devs Name](https://other-devs-webpage.com/) |
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put your and my name in here for now?
| # An example documentation | ||
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| This is a sample text to outline the structure of the packages in the `Experimental` folder. | ||
| You can show docstrings like this: | ||
| ```@docs | ||
| my_access_func(S::ExampleStruct) | ||
| ``` |
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As @thofma's question showed, it's probably a good idea to put in a sentence or two. For now it doesn't have to be much, but at least that this is about linear algebraic groups, and what is meant by that.
And perhaps we really want this to be about reductive linear algebraic groups ... See also e.g. section 2.2 of Derksen & Kemper, Computational Invariant Theory, 2015.
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In particular, have a look at the text at the start (before section 2.2.1 starts), then Definition 2.2.1 and finally Example 2.2.18 (feel free to look at more, but that's the only two things I meant by the above; perhaps a glance at the start of section 2.2.2 might be interesting in that it connects it to the notion of "reductive group" you might see in Malle-Testermann)
| # Linear Algebraic Groups | ||
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| function linear_algebraic_group(rs::RootSystem, k::Field) |
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Note to others who might see this and wonder: the plan is to eventually support arbitrary (finite/spherical) root data, but those are not yet implemented, so this is a start.
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This is part of my Bachelor Thesis supervised by Annette Bachmayr and @fingolfin.
At the moment I am mostly interested in the comments of @fingolfin, but feel free to leave comments.