Symplectic, orthogonal and linear Lie groups in Clifford algebra

Abstract

In this paper we prove isomorphisms between 5 Lie groups (of arbitrary dimension and fixed signatures) in Clifford algebra and classical matrix Lie groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms of corresponding Lie algebras.

References in corpus (5)

• Unitary spaces on Clifford algebras
• Quaternion typification of Clifford algebra elements
• 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
• A symplectic subgroup of a pseudounitary group as a subset of Clifford algebra

Cited by in corpus (8)

• Classification of Lie algebras of specific type in complexified Clifford algebras
• 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 Lie Groups Preserving Subspaces of Degenerate Clifford Algebras