TL;DR
This paper explores the categorical relationships between Lie algebras derived from group algebras and Plesken Lie algebras, providing examples involving subgroups of the Heisenberg group.
Contribution
It describes the categories of Lie algebras of group algebras and Plesken Lie algebras, and investigates their interrelations with concrete examples.
Findings
Categorical relations between Lie algebras of group algebras and Plesken Lie algebras established.
Examples involving subgroups of the Heisenberg group illustrate these categories.
The structure of Lie algebras associated with specific subgroups analyzed.
Abstract
In this paper we describe the the category of Lie algebras of group algebras and the category of Plesken Lie algebras and explore the categorical relations between them. Further we provide the examples of the Lie algebra of the group algebra of subgroups of Heisenburg group and the Plesken Lie algebra of subgroups of Heisenburg group.
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