# Classification of Lie algebras of specific type in complexified Clifford algebras

## TL;DR

This paper provides a comprehensive classification of sixteen specific Lie algebras within complexified Clifford algebras, establishing their isomorphisms with classical matrix Lie algebras and exploring their relation to spin groups.

## Contribution

It introduces a complete classification of certain Lie algebras in complexified Clifford algebras and links them to classical matrix Lie algebras and spin groups.

## Key findings

- Sixteen Lie algebras classified as direct sums of quaternion-type subspaces.
- Isomorphisms established with classical matrix Lie algebras across dimensions.
- Connection between these Lie groups and spin groups analyzed.

## 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.