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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTime7 days ago

I tried to edit the entry double derivation and even if I write a single letter or none (!) it sends back an error

500 Internal Server Error

Your edit was blocked by spam filtering

Please report this on the nForum in the nLab Technical Matters category. Please give as precise details as you can as to what triggered the error.

Here is the error:

No such file or directory @ rb_sysopen - page_content/submitted_edits/nlab/double_derivation

etc. If I try to click on “discuss” button it does NOT open the latest changes page but just links to front page of $n$Forum, not linked to a page.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTime7 days ago
Here is the edited page which I did not succeed to send:

Given a _commutative_ ring $k$ and an associative $k$-algebra $A$ over $k$, the tensor product $A\otimes_k A$ is equipped with two bimodule structures, "outer" and "inner". For the outer structure $a\cdot_o(b\otimes c)\cdot_o d = a b\otimes c d$ and for the inner $a\cdot_i(b\otimes c)\cdot_i d = b d\otimes a c$. The two bimodule structures mutually commute. A $k$-linear map $\alpha\in Hom_k(A,A\otimes A)$ is called a __double derivation__ if it is also a map of $A$-bimodules with respect to the _outer_ bimodule structure ($\alpha\in A Mod A({}_A A_A,{}_A A\otimes_k A_A)$); thus the $k$-module $Der(A,A\otimes A)$ of all double derivations becomes an $A$-bimodule with respect to the _inner_ $A$-bimodule structure.

The tensor algebra $T_A Der(A,A\otimes A)$ of the $A$-bimodule $Der(A,A\otimes A)$ (which is the free monoid on $Der(A,A\otimes A)$ in the monoidal category of $A$-bimodules) is a step in the definition of the deformed preprojective algebras of Bill Crawley-Boevey. A theorem of Van den Bergh says that for any associative $A$ the tensor algebra $T_A Der(A,A\otimes A)$ has a canonical double Poisson bracket.

* Michel Van den Bergh, _Double Poisson algebras_, Trans. Amer. Math. Soc. __360__ (2008) 5711--5769, [arXiv:math.AG/0410528](https://arXiv.org/abs/math/0410528)
* Anne Pichereau, Geert Van de Weyer, _Double Poisson cohomology of path algebras of quivers_, J. Alg. __319__, 5 (2008) 2166--2208 [doi](https://doi.org/10.1016/j.jalgebra.2007.09.021)
* Jorge A. Guccione, Juan J. Guccione, _A characterization of quiver algebras based on double derivations_, [arXiv:0807.1148](https://arxiv.org/abs/0807.1148)

category: algebra
• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTime7 days ago
Copying the content of double derivation to another pagename does not work: spam message appears instead of creating a page, including at my personal web.

I created William Crawley-Boevey with redirect Bill Crawley-Boevey wanted at double derivation which still shows that Bill Crawley-Boevey does not exist.
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTime6 days ago

Have been busy all day. Am forwarding this to the technical team now…

1. The problem was that "gucci" was a pattern in the spam filter. I've removed it. You should now be able to submit your edit.
• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTime5 days ago

Unfortunately, it still seem to persist if I leave “Guccione” so I temporarily wrote G uccione with a space. Then it accepts.

• V. Ginzburg, T. Schedler, Differential operators and BV structures in noncommutative geometry, Sel. Math. New Ser. 16, 673–730 (2010) doi
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTime5 days ago

One can work around this problem by escaping some html characters. For example:

  &#71;uccione


gives

Guccione

2. Unfortunately, it still seem to persist if I leave “Guccione”

Right, I forgot to actually update the deployment. Should be fixed now.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTime5 days ago

7 thanks for the tip