Comments on: From the Da Vinci code to Galois https://lievenlebruyn.github.io/neverendingbooks/from-the-da-vinci-code-to-galois/ Sat, 31 Aug 2024 11:35:28 +0000 hourly 1 https://wordpress.org/?v=6.6.1 By: lievenlb https://lievenlebruyn.github.io/neverendingbooks/from-the-da-vinci-code-to-galois/#comment-88 Wed, 31 Jan 2018 07:12:24 +0000 http://www.neverendingbooks.org/?p=7868#comment-88 Asvin, in the paper Larson and Taft describe he case over algebraically closed fields, and as the continuous dual behaves under extension of scalars, Galois descent gives it over any field. Some more details about the (algebraically closed) field case can be found in Peterson-Taft The Hopf algebra of linearly recursive sequences.

For the integral case, you can for example look at this paper. But, probably i’ll write some follow-up posts soon.

]]> By: Asvin https://lievenlebruyn.github.io/neverendingbooks/from-the-da-vinci-code-to-galois/#comment-87 Wed, 31 Jan 2018 02:19:59 +0000 http://www.neverendingbooks.org/?p=7868#comment-87 Hi,
I took a look at the reference you mentioned and they do not seem to treat the integral case or mention any connection with the absolute Galois group.

I guess you will write about it in the next post but could you suggest a reference for the integral/number theoretic stuff?

]]> By: lievenlb https://lievenlebruyn.github.io/neverendingbooks/from-the-da-vinci-code-to-galois/#comment-86 Mon, 29 Jan 2018 07:37:07 +0000 http://www.neverendingbooks.org/?p=7868#comment-86 I think the standard notation for the complex group algebra of a group $G$ is $\mathbb{C} G$, but in this case with the two \overline ‘s it is a bit confusing so I changed it. Thanks!

]]> By: David Roberts https://lievenlebruyn.github.io/neverendingbooks/from-the-da-vinci-code-to-galois/#comment-85 Mon, 29 Jan 2018 00:18:52 +0000 http://www.neverendingbooks.org/?p=7868#comment-85 >the group-algebra of the multiplicative group of non-zero elements

should this be denoted \Qbar[\Qbar^*_\times]? As stated it looks like a typo 🙂

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