Reduced contragredient Lie algebras and PC Lie algebras
Nagatoshi Sasano
TL;DR
This paper demonstrates how finite-dimensional reductive Lie algebras and their representations can be embedded into PC Lie algebras and explores the structural properties of PC Lie algebras.
Contribution
It introduces a method to embed reductive Lie algebras into PC Lie algebras and analyzes their structure, advancing understanding of their algebraic relationships.
Findings
Reductive Lie algebras can be embedded into PC Lie algebras.
The structure of PC Lie algebras is characterized.
Representation theory of reductive Lie algebras is connected to PC Lie algebras.
Abstract
The first aim of this paper is to show that any finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation can be embedded into some PC Lie algebra. The second aim is to find the structure of a PC Lie algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra