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Topic: Spin(8)

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	Spin(0,8) Physics (Site not responding. Last check: 2007-11-04)
		The Coxeter-Dynkin diagram of Spin(8) is shown in red.
		Begin with the 28 infinitesimal generators of Spin(8).
		The 28 can be represented on a 1-dimensional space by mapping each of the 28 into +1.
	www.valdostamuseum.org /hamsmith/Spin8.html (1411 words)

	SO(8) - Wikipedia, the free encyclopedia
		This gives rise to peculiar feature of Spin(8) known as triality.
		Related to this is the fact that the two spinor representations, as well as the fundamental vector representation, of Spin(8) are all eight-dimensional (In all other dimensions the spinor representation is either smaller or larger than the vector representation).
		The triality automorphism of Spin(8) is the outer automorphism group of Spin(8) which is isomorphic to the symmetric group S
	en.wikipedia.org /wiki/SO(8) (208 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		> Spin(8), and its relation to the Clifford algebra CL_8,
		Lie algebra of Spin(8), not for the Lie group Spin(8).
		Third, all research on triality, an exceptional phenomenom,
	www.mathforum.org /kb/plaintext.jspa?messageID=259633 (313 words)

	SO(8) - Definition, explanation (Site not responding. Last check: 2007-11-04)
		The universal cover of SO(8) is the spinor group Spin(8).
		Related to this is the fact that the two spinor representations, as well as the fundamental vector representation, of Spin(8) are all eight-dimensional (In all other dimensions the spinor representation is either smaller or larger than the vector representation).
		The triality automorphism of Spin(8) is the outer automorphism group of Spin(8) which is isomorphic to the symmetric group S
	www.calsky.com /lexikon/en/txt/s/so/so_8_.php (554 words)

	[No title]
		The group Spin(8) has three 8-dimensional irreducible representations: the vector, left-handed spinor, and right-handed spinor representation.
		Note that Cliff and S are representations of Cliff by left multiplication, and therefore are representations of Spin(8) --- because Spin(8) sits inside Cliff.
		Now, since any element of Cliff that's in Spin(8) has even degree in Cliff, and since even times even is even, while even times odd is odd, it follows that as a representation of Spin(8), S splits into S+ and S-, which we call the left-handed and right-handed spinors, respectively.
	math.ucr.edu /home/baez/twf_ascii/week61 (3033 words)

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