Continuous Groups with Antilinear Operations

TL;DR

This paper introduces a new class of continuous groups combining Lie groups with antilinear operations, defining their matrix algebras and exploring their algebraic structure and consistency conditions.

Contribution

It defines continuous groups of the form G + a_0G with antilinear operations and analyzes their associated matrix algebras and structural constants.

Findings

Defined groups of the form G + a_0G with antilinear operations

Established the structure of matrix algebras for these groups

Derived conditions on structural constants from Jacobi identities

Abstract

Continuous groups of the form: $G+a_0G$ are defined, where $G$ denotes a Lie group and $a_0$ denotes an antilinear operation which fullfils the condition $a^2_0=\pm 1$. The matrix algebras connected with the groups $G+a_0G$ are defined. The structural constants of these algebras fulfill the conditions following from the Jacobi identities.