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SemiSpin(16) in nLab

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Context

Higher spin geometry

Group Theory

group theory

Classical groups

Finite groups

Group schemes

Topological groups

Lie groups

Super-Lie groups

Higher groups

Cohomology and Extensions

Related concepts

Higher Lie theory

∞-Lie theory (higher geometry)

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Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

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Cohomology

Homotopy

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Examples

∞\infty-Lie groupoids

∞\infty-Lie groups

∞\infty-Lie algebroids

∞\infty-Lie algebras

Contents

Idea

The semi-spin group in dimension 16.

Properties

As a subgroup of E 8E_8

The subgroup of the exceptional Lie group E8 which corresponds to the Lie algebra-inclusion 𝔰𝔬(16)↪𝔢 8\mathfrak{so}(16) \hookrightarrow \mathfrak{e}_8 is the semi-spin group in that dimension

SemiSpin(16)⊂E 8 SemiSpin(16) \;\subset\; E_8

On the other hand, the special orthogonal group SO(16)SO(16) is not a subgroup of E 8E_8 (e.g. McInnes 99a, p. 11).

In heterotic string theory

In heterotic string theory with gauge group the direct product group E 8×E 8E_8 \times E_8 it is usually only this subgroup Semispin(16)×SemiSpin(16)Semispin(16) \times SemiSpin(16) which is considered (but typically denoted Spin(16)/ℤ 2Spin(16)/\mathbb{Z}_2, see also Distler-Sharpe 10, Sec. 1).

References

Created on May 8, 2019 at 15:48:51. See the history of this page for a list of all contributions to it.