*-Lie-Type maps on alternative *-algebras

TL;DR

This paper characterizes multiplicative *-Lie-type maps on alternative *-algebras and applies the results to alternative W*-algebras, advancing understanding of their structure.

Contribution

It provides a new characterization of *-Lie-type maps on alternative *-algebras, including applications to W*-algebras.

Findings

Characterization of multiplicative *-Lie-type maps

Application to alternative W*-algebras

Enhanced understanding of algebraic structure

Abstract

Let $A$ and $A'$ be two alternative $*$-algebras with identities 1_A and 1_A', respectively, and e_1 and e_2 = 1_A - e_1 nontrivial symmetric idempotents in A. In this paper we study the characterization of multiplicative *-Lie-type maps. As application, we get a result on alternative W*-algebras.