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Classification of Lie algebras of specific type in complexified Clifford algebras. (English) Zbl 1393.17034
Summary: We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These 16 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 16 Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups.

MSC:
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
15A66 Clifford algebras, spinors
22E60 Lie algebras of Lie groups
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