标题： 关于包含自旋群的某些李群在 Clifford 代数中 显示英文标题

标题： On some Lie groups containing spin group in Clifford algebra

摘要： 在本文中，我们考虑复化 Clifford 代数中的一些李群。 利用 Clifford 代数中共轭运算与矩阵运算之间的关系，我们在任意维度和任意符号的情况下，证明了这些群与经典矩阵群（辛、正交、线性、酉）之间的同构。 此外，我们还得到了相应李代子代数的同构，这些李代子代数是四元数类型子空间的直和。 自旋群是所有考虑群的一个子群，并在$n\leq 5$的情况下与其中一个群重合。 我们给出了包含自旋群的经典矩阵李群，在任意维度的情况下。 显示英文摘要

摘要： In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups (symplectic, orthogonal, linear, unitary) in the cases of arbitrary dimension and arbitrary signature. Also we obtain isomorphisms of corresponding Lie algebras which are direct sums of subspaces of quaternion types. Spin group is a subgroup of all considered groups and it coincides with one of them in the cases $n\leq 5$. We present classical matrix Lie groups that contain spin group in the case of arbitrary dimension.