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2006•Journal of Jiamusi UniversityRequires access

Additive Rank 1 Preservers between Hermitian Matrix Space over Dimension Rings

Han Jing-wen

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Abstract

Let D be a division ring which possesses an involution.Denote by H_n(D) the space of n×n Hermitian matrices over D.In this paper,the authors characterize the additive maps from H_n(D) into H_m(D) that preserve rank 1 in some addition.As an application,the additive maps that preserve the general linear group over H_n(D) are further characterized.

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What this paper is about

Let D be a division ring which possesses an involution.Denote by H_n(D) the space of n×n Hermitian matrices over D.In this paper,the authors characterize the additive maps from H_n(D) into H_m(D) that preserve rank 1 in some addition.As an application,the additive maps that preserve the general linear group over H_n(D) are further characterized.

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Available abstract

Let D be a division ring which possesses an involution.Denote by H_n(D) the space of n×n Hermitian matrices over D.In this paper,the authors characterize the additive maps from H_n(D) into H_m(D) that preserve rank 1 in some addition.As an application,the additive maps that preserve the general linear group over H_n(D) are further characterized.

Key concepts: Hermitian matrix, Mathematics, Division ring, Rank (graph theory), Involution (esoterism), Dimension (graph theory), Pure mathematics, Combinatorics

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