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Revision as of 18:37, 9 February 2014

Arbitration clarification request closed

This is a message to inform you that a request for clarification has now been closed and following motion has been passed. The Arbitration Committee resolves by motion that

In May 2012 (during the Race and intelligence review), the committee prohibited SightWatcher (talk · contribs) from "participating in any discussion concerning the conduct of editors who have worked in the topic" – and therefore from discussing Mathsci's conduct. In October 2012, The Devil's Advocate (talk · contribs) and Cla68 (talk · contribs) were banned (by an administrator acting under discretionary sanctions) from interacting with Mathsci. In December 2012, Mathsci was prohibited (again under discretionary sanctions) by an arbitration enforcement administrator from requesting enforcement of these interaction bans without prior permission. The Arbitration Committee has decided to change these from one-way to two-way interaction bans. Accordingly, Mathsci (talk · contribs) is indefinitely prohibited from:

• Commenting on, or interacting with, The Devil's Advocate (talk · contribs)
• Commenting on, or interacting with, Cla68 (talk · contribs)
• Participating in any discussion concerning the conduct of SightWatcher (talk · contribs).

This motion should be enforced under the enforcement clauses of the Race and intelligence final decision.

For the Arbitration Committee, Callanecc (talk • contribs • logs) 09:14, 17 September 2013 (UTC)

AE request concerning you

Hello. An enforcement request concerning you has been made at Misplaced Pages:Arbitration/Requests/Enforcement#Mathsci. Please make a statement there. Thanks,  Sandstein  10:19, 4 October 2013 (UTC)

Please add any statement you wish to make to that section within 24 hours, i.e., until 07:30, 6 October 2013 (UTC). If you choose not to make a statement within that time frame, the request may be acted upon regardless.  Sandstein  07:20, 5 October 2013 (UTC)

ArbCom Clarification request concerning you

Hello. A clarification request concerning you has been made here. Please make a statement there. Thank you. Cla68 (talk) 23:10, 6 October 2013 (UTC)

Arbitration clarification request closed

This is a message to inform you that a request for clarification has now been closed and following motion has been passed. The Arbitration Committee resolves by motion that

For posting inappropriate material relating to an editor with whom he is subject to an interaction restriction, Mathsci is indefinitely banned from the English Misplaced Pages. He may request reconsideration of the ban not less than six months from the date this motion passes.

For the Arbitration Committee, Rschen7754 09:05, 13 October 2013 (UTC)

As an administrator, I have implemented the remedy above. --Rschen7754 09:06, 13 October 2013 (UTC)

Sorry to see this Mathsci. Hope you'll try to come back after the six month period. Use the time wisely in RL!--regentspark (comment) 13:45, 13 October 2013 (UTC)

@RegentsPark: I noticed that you're running for election again and that you are well over 18. Both of those are good things ... or are they? Good luck anyway!

I also noticed that the image on my user page taken in the Cemetery at La Treille was already on Commons. Another image uploaded simultaneously had not been transferred, so I did it manually. Surprisingly within a few hours the image showed up on www.geolocation.ws. Both images are of high quality even if they were taken on a cloudy Sunday morning in March. Mathsci (talk) 08:05, 17 November 2013 (UTC)

File:Samuel-Palmer-magic-apple-tree.png listed for deletion

A file that you uploaded or altered, File:Samuel-Palmer-magic-apple-tree.png, has been listed at Misplaced Pages:Files for deletion. Please see the discussion to see why it has been listed (you may have to search for the title of the image to find its entry). Feel free to add your opinion on the matter below the nomination. Thank you. ALH (talk) 00:46, 14 January 2014 (UTC)

Comments on mutations of alternative algebras

Mutations of Jordan algebras arise naturally when using Jordan algebras as a framework for constructing Hermitian symmetric spaces of compact type. Alternative algebras arise in the classification of Jordan algebras and their generalisations. In particular the product a*b = ab + ba on an alternative algebra makes it into a Jordan algebra (McCrimmon nicknames this the "plus construction"); and the Peirce decomposition gives a construction of alternative algebras in the reverse direction. So it is natural that there should be a correspondence between appropriate classes of isotopies, etc.

The main references for the topic are

• Adrian Albert's 1943 Annals paper on isotopy of non-associative algebras
• Kevin McCrimmon's 1971 paper in Math. Annalen on Mutations of alternative algebras
• Ottmar Loos' 1975 Springer Lecture Notes on Jordan pairs
• Holger Petersson's 2002 paper on the structure group of an alternative algebra

Most of this is explained in Loos' tersely written lecture notes on Jordan pairs, which contain a parallel treatment of alternative pairs. By introducing the notion of pair, isotopy transforms into isomorphisms of pairs and the structure group as a Jordan algebra or alternative algebra becomes natural in this setting. The homotopes for alternative algebras involved are those defined by McCrimmon. These change the product from xy to (xa)(by). These are related to Albert's original definition and also (by Petersson's work) to the structure group. The book of Elduque and Myung (which can be found in its entirety on bookza.org) treats a broader class of isotopies of alternative algebras than those defined by McCrimmon; but only the isotopies of McCrimmon are compatible with Jordan algebra structures. The book of Elduque and Myung unfortunately does not contain a summary of the main results outlined in McCrimmon, Loos et al. (Its purpose was somewhat different.) It would theoretically be possible to give a complete account of the theory of mutations of alternative algebras in a wikipedia article using the above sources as a guide. One slight minus—which would discourage many, including me, from writing anything about the subject—is that there don't seem to be any significant applications elsewhere, unlike the Jordan algebra case (cf Max Koecher's 1970 invited ICM address in Nice on "Jordan algebras and differential geometry"). All of the references, however, are available in their entirety on the web. That is a slight plus for would-be editors. Mathsci (talk) 18:37, 9 February 2014 (UTC)