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LSpice
LSpice
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Relation between positive roots of $E_8$ and $\mathbb{F}_2^8 /\setminus \{00\}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the Latticelattice $E_7$ and $\mathbb{F}_2^6/{0}$$\mathbb{F}_2^6 \setminus \{0\}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is also a relation between $E_8$ and $\mathbb{F}_2^8/{0}$$\mathbb{F}_2^8 \setminus \{0\}$. Is there an explicit description of the features of this relation in the literature?

Relation between positive roots of $E_8$ and $\mathbb{F}_2^8 /{0}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the Lattice $E_7$ and $\mathbb{F}_2^6/{0}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is also a relation between $E_8$ and $\mathbb{F}_2^8/{0}$. Is there an explicit description of the features of this relation in the literature?

Relation between positive roots of $E_8$ and $\mathbb{F}_2^8 \setminus \{0\}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the lattice $E_7$ and $\mathbb{F}_2^6 \setminus \{0\}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is also a relation between $E_8$ and $\mathbb{F}_2^8 \setminus \{0\}$. Is there an explicit description of the features of this relation in the literature?

deleted 33 characters in body; edited title
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IMeasy
IMeasy
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Bijection Relation between positive roots of $E_8$ and $\mathbb{F}_2^8 /{0}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the Lattice $E_7$ and $\mathbb{F}_2^6/{0}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is also a similar bijectionrelation between $E_8$ and $\mathbb{F}_2^8/{0}$, that preserves orthogonality. Is there any "Cayley like" explicitan explicit description of the features of this bijectionrelation in the literature?

Bijection between positive roots of $E_8$ and $\mathbb{F}_2^8 /{0}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the Lattice $E_7$ and $\mathbb{F}_2^6/{0}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is a similar bijection between $E_8$ and $\mathbb{F}_2^8/{0}$, that preserves orthogonality. Is there any "Cayley like" explicit description of this bijection in the literature?

Relation between positive roots of $E_8$ and $\mathbb{F}_2^8 /{0}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the Lattice $E_7$ and $\mathbb{F}_2^6/{0}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is also a relation between $E_8$ and $\mathbb{F}_2^8/{0}$. Is there an explicit description of the features of this relation in the literature?

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IMeasy
IMeasy
  • 3.8k
  • 22
  • 37

Bijection between positive roots of $E_8$ and $\mathbb{F}_2^8 /{0}$

There exists an explicit bijection (due to Cayley, that has built up a very nice table to describe this) between the positive roots of the Lattice $E_7$ and $\mathbb{F}_2^6/{0}$ (where $\mathbb{F}_2$ is the field with two elements. Btw, this also preserves orthogonality. There is a similar bijection between $E_8$ and $\mathbb{F}_2^8/{0}$, that preserves orthogonality. Is there any "Cayley like" explicit description of this bijection in the literature?