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now gives lots of explicit detail on how to construct Hopf algebras from generic tensor products (exterior product, symmetric product, etc). At the bottom is a short section that briefly mentions the divided-power Hopf algebra. What you (or someone) would need to do is to go through the same steps,
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but now for the divided power algebra, and to then replace the tensor by the symmetric product, and thus gain the insight you are looking for ... It probably would not be a bad idea to expand this article to do all this.
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554:{\displaystyle (\phi \psi )(x_{1}\cdots x_{n})=\sum _{S\subseteq \{1,2,\ldots ,n\}}\phi \left(\prod _{i\in S}x_{i}\right)\psi \left(\prod _{j\notin S}x_{j}\right).}
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Somebody more experienced than I am please check the formatting for the references section. Do I need to put a link to the reference somewhere near the beginning?
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Addition is just the normal pointwise addition of functions. For multiplication, given
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I'm wondering whether it would be worth it to indicate exactly what the PD structure on
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can easily be seen to be an ideal with respect to this ring structure. Then defining
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parts, thus making the above definition of the PD structure a natural one.)
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is, or whether it is a bit too complex and would obscure things.
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Be more specific on the dual-to-symmetric-algebra example?
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668:{\displaystyle \gamma _{m}\phi :S^{\cdot }M\to A}
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228:If I included it, it would go something like:
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