I know the properties and most things about, but the Space they live I do not know the name, I find it strange not to have a name just hear that are kind of such a space, in some places until I heard that the space of spinors had the name of internal space, and I found nothing about, someone know the name?
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I've heard "the space of quaternions" – Dan Uznanski Jul 28 '21 at 10:26
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@Ian, welcome to MSE. Maybe you want to read this first. Here is a more accurate quote from Sir Michael Atiyah: "No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the 'square root' of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors." – Kurt G. Jul 28 '21 at 12:05
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So your spaces don't really have a specific name? – Ian Jul 28 '21 at 12:28
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I have a hard time parsing the question, but it seems there is a misunderstanding: The quaternions $\mathbb{H}$ are a space, they don't "live in" some larger space. The same is true of spinors, generally speaking, though the term "spinor" can refer to several different things. – Kajelad Jul 28 '21 at 22:01
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the spinors they live in which space? – Ian Jul 29 '21 at 10:20
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In the fundamental representation of the Clifford algebra. In Kajelad's more rigorous language: they don't 'live' there. They are that space. – Kurt G. Jul 29 '21 at 15:19