$*$-Lie-type maps on $C^*$-algebras
Ruth Nascimento Ferreira, Bruno Leonardo Macedo Ferreira, Henrique, Guzzo Junior, Bruno Tadeu Costa

TL;DR
This paper characterizes multiplicative $*$-Lie-type maps on $C^*$-algebras, showing that in factor von Neumann algebras such maps are necessarily $*$-isomorphisms, thus revealing their structural nature.
Contribution
It provides a characterization of multiplicative $*$-Lie-type maps on $C^*$-algebras, especially demonstrating their equivalence to $*$-isomorphisms in factor von Neumann algebras.
Findings
Every bijective unital multiplicative $*$-Lie-type map on a factor von Neumann algebra is a $*$-isomorphism.
The paper characterizes these maps in terms of algebraic structure preservation.
It extends the understanding of $*$-Lie-type maps in the context of operator algebras.
Abstract
Let and be two -algebras with identities and , respectively, and and nontrivial symmetric projections in . In this paper we study the characterization of multiplicative -Lie-type maps. In particular, if is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative -Lie-type map is -isomorphism.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Algebraic structures and combinatorial models
