On crossed product of algebras

TL;DR

This paper explores the concept of crossed tensor products of algebras, examining related constructions, representations, and applications in noncommutative geometry and particle systems with generalized statistics.

Contribution

It introduces and analyzes crossed tensor products of algebras, discusses crossed enveloping algebras, and connects these concepts to applications in noncommutative geometry and physics.

Findings

Development of the theory of crossed tensor products

Analysis of crossed enveloping algebras and their representations

Applications to noncommutative geometry and generalized particle statistics

Abstract

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative geometry and particle systems with generalized statistics are indicated.