# Talk:Real form (Lie theory)

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Field: Algebra

## Move?

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

Not moved. Vegaswikian (talk) 20:41, 8 December 2009 (UTC)

• There is no ambiguity in “Real form”, and no other “Real form (qualifier)” pages, as Special:PrefixIndex/Real form shows (they are just redirects to the same page). Thanks!   —Nils von Barth (nbarth) (talk) 22:00, 1 December 2009 (UTC)
• Oppose. There are lots of things in many fields of experience that could be called real forms or similar, as distinguished from apparent or unreal or falsified or erroneous etc etc forms or shapes or varieties etc. The disambiguator is needed. Anthony Appleyard (talk) 23:15, 1 December 2009 (UTC)
• Oppose In mathematics, the notion of a "real form" relates objects defined over the field of real and complex numbers. IOW, there are real forms for things other than Lie groups, like other parts of mathematics... Spherical harmonics, Solid harmonics, etc. Additionally, per Anthony Appleyard, there are uses outside of mathematics. Further in English "real form" is synonymous with "true form". 76.66.203.178 (talk) 04:53, 2 December 2009 (UTC)
• Oppose. Many other objects throughout mathematics have real forms, algebraic varieties and associative algebras being the most common examples. As 76.66.203.178 pointed out, one can speak of "real forms" whenever we can compare an object over the fields of real and complex numbers. Arcfrk (talk) 02:03, 4 December 2009 (UTC)
• Comment. Isn't "form" a technical term in algebra? More precisely, if some algebra (Lie algebra or associative one) B is isomorphic to $A \otimes_k K$, then A is a k form of B. If k is the set of real numbers, then A is a real form. (At least that's how I was taught in my algebra course.) If so, "real form" in Lie theory is simply a special case, and what we need an actual article on "form" (real being some specific example) -- Taku (talk) 03:27, 4 December 2009 (UTC)
• Correct. But the main purpose of this article is to explain the classification of real forms of semisimple Lie algebras. Analogous material for associative and alternative algebras includes quaternions and classification of real forms of the Cayley algebra, but I don't think either one grants an independent article. Classification of forms for semisimple algebraic groups over a more general field is a tricky business, even for non-archimedean local fields, and certainly for number fields (cf Platonov–Rapinchuk). Arcfrk (talk) 14:56, 4 December 2009 (UTC)
The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.