Stability of the E8-form (Ex)
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$\langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle -1 \rangle \cong ({\mathbb Z}^8,\lambda) \oplus \langle -1 \rangle$ | $\langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle -1 \rangle \cong ({\mathbb Z}^8,\lambda) \oplus \langle -1 \rangle$ | ||
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| + | where $\lambda$ is unimodular, even, and positive definite. | ||
Revision as of 06:02, 8 January 2019
Show there exists an isometry of unimodular forms
where 
is unimodular, even, and positive definite.
