Knowlpedia

Definition

SO(5,R)

SO(5,R) as a separately identified real Lie group, with its defining operations and dimension.

SO⁡(5,R)\operatorname{SO}(5,\mathbb R) is the of R5\mathbb R^{5} for the ∑jxjyj\sum_jx_jy_j:

SO⁡(5,R)={A∈M5(R):ATA=I, det⁡A=1}.\operatorname{SO}(5,\mathbb R)=\{A\in M_{5}(\mathbb R):A^{\mathsf T}A=I,\ \det A=1\}.
Dimensions and structure

This group has real dimension 1010. Its tangent algebra is the skew-symmetric 5×55\times5 matrices. The spin covering has kernel {±1}, so this group is not .

References
  1. Pavel Etingof, Lie Groups and Lie Algebras (MIT lecture notes), §31.2, Example 31.3 and Proposition 31.4; §31.3, Example 31.10, pp. 166–168.