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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 5th 2011

created stub for Jordan-Lie-Banach algebra

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeOct 13th 2013

I added a definition from the top reference. I modified it to use only $r = 1$ in the associator identity; I can't tell what good it does to allow other values of $r$, and in any case, the construction of a JLB-algebra from a $C^*$-algebra (which is supposed to be an equivalent notion!) always produces $r = 1$.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeOct 13th 2013

Thanks!

I have also cross-linked that entry now with order-theoretic structure in quantum mechanics.

• CommentRowNumber4.
• CommentAuthorTobyBartels
• CommentTimeAug 8th 2020

Explain what Halvorson's $r$ is doing.

• CommentRowNumber5.
• CommentAuthorTobyBartels
• CommentTimeOct 1st 2020
• (edited Oct 1st 2020)

What I had for the norm on $A + \mathrm{i}A$ was wrong, and it was really hard to figure out how to define it from the norm on $A$. In general, it may not be possible. But we really care about the $C^*$-case, and there the norm is defined by the algebraic structure, so let's just punt on it.

ETA: If you want to look at the diff, then also look at the previous diff, which actually has most of what I changed today.