In this article, we treat the space $\mathbb{H}$ of real quaternions as a Lie algebra equipped with its commutator product. We show that all involutions of this Lie algebra that are automorphisms (respectively, anti-automorphisms) and restrict to the identity on the centre $\mathbb{R}\cdot 1$ (sometimes called automorphisms of the first kind) are actually algebra automorphisms (resp. anti-automorphisms) of the division algebra of quaternions, which we characterized in an earlier paper. If we compose with scalar multiplication by $-1$, we obtain all involutive automorphisms and anti-automorphisms of the second kind, i.e. those for which the centre is contained in the $-1$-eigenspace. Together, we have a complete determination of all involutive (anti-)automorphisms on the quaternionic Lie algebra $L(\mathbb{H})$. From this determination of all the involutive (anti-)automorphisms of $L(\mathbb{H})$, one can identify via a standard bijective correspondence all the involutive (anti-)automorphisms for the corresponding simply connected multiplicative quaternion Lie group $\mathbb{H}-\{0\}$. We carry out this determination explicitly.

在这篇文章中，我们对待空间$\mathbb{H}$实四元数的李代数及其换向器积。我们证明了这个李代数的所有对合都是自同构（分别是反自同构）并且限制在中心的身份$\mathbb{R}\cdot \mathrm{1个}$（有时称为第一类自同构）实际上是四元数除法代数的代数自同构（resp。反自同构），我们在较早的论文中对其进行了表征。如果我们用标量乘法组合$-\mathrm{1个}$, 我们得到所有的第二类对合自同构和反自同构, 即那些中心包含在$-\mathrm{1个}$-本征空间。我们一起完全确定了四元李代数上的所有对合（反）自同构$\mathrm{大号}(\mathbb{H})$. 从所有对合（反）自同构的确定$\mathrm{大号}(\mathbb{H})$, 可以通过标准的双射对应识别对应的单连通乘法四元数李群的所有内合（反）自同构$\mathbb{H}-\{0\}$. 我们明确执行此确定。