The Infinitesimal-Operator Algebras of Continuous Groups with Antilinear Operations

TL;DR

This paper develops the theory of infinitesimal-operator algebras for continuous groups that include antilinear operations, extending previous work on their matrix algebras.

Contribution

It introduces and analyzes the properties of infinitesimal-operator algebras for groups combining linear and antilinear operations, generalizing earlier matrix algebra results.

Findings

Defined infinitesimal-operator algebras for groups with antilinear operations

Determined properties of these algebras

Extended previous matrix algebra results to a broader class of groups

Abstract

Continuous groups with antilinear operations of the form $G+a_0G$, where $G$ denotes a linear Lie group, and $a_0$ is an antilinear operation which fulfills the condition $a^2_0=\pm 1$, were defined and their matrix algebras were investigated in \cite{Kocinski4}. In this paper infinitesimal-operator algebras are defined for any group of the form $G+a_0G$, and their properties are determined.