Classification of Lie algebras of specific type in complexified Clifford algebras

Abstract

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present sixteen Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups.

arXiv comment18 pages, 1 figure

References in corpus (8)

• Unitary spaces on Clifford algebras
• Quaternion typification of Clifford algebra elements
• On the transposition anti-involution in real Clifford algebras I: The transposition map
• On the transposition anti-involution in real Cliffrd algebras II: Stabilizer groups of primitive idempotents
• A classification of Lie algebras of pseudounitary groups in the techniques of Clifford algebras
• Development of the method of quaternion typification of Clifford algebra elements
• On some Lie groups containing spin group in Clifford algebra
• Symplectic, orthogonal and linear Lie groups in Clifford algebra

Cited by in corpus (11)

• On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension
• Clifford algebras and their applications to Lie groups and spinors
• Subgroups of Clifford algebras
• Covariantly constant solutions of the Yang-Mills equations
• On generalization of Lipschitz groups and spin groups
• On inner automorphisms preserving subspaces of Clifford algebras
• On Some Lie Groups in Degenerate Clifford Geometric Algebras
• On SVD and Polar Decomposition in Real and Complexified Clifford Algebras
• On Rank of Multivectors in Geometric Algebras
• Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras
• On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras