Projectivity and injectivity of $\mathsf{G}$-Hilbert $\Im$-modules

Journal of Linear and Topological Algebra

دوره 12، شماره 03، دی 2023، صفحه 163-177   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.1992299.1578

نویسندگان

A. Yousefi¹؛ M. R. Mardanbeigi^{* 2}

¹Department of Mathematics‎, ‎Faculty of Science‎, ‎Science and Research Branch‎, ‎Islamic Azad University (IAU)‎, ‎Tehran‎, ‎Iran

²Department of Mathematics‎, ‎Faculty of Science‎, ‎Science and Research Branch‎, ‎Islamic Azad University (IAU)‎, ‎Tehran‎, ‎Iran

چکیده

‎Let $\mathsf{G}$ be a discrete group acting on $C^*$-algebra $\Im$‎. ‎In this paper‎, ‎we investigate projectivity and injectivity of $G$-Hilbert $\Im$-modules and study the equivalent conditions characterizing $\mathsf{G}$-$C^*$-subalgebras of the algebra of compact operators on $\mathsf{G}$-Hilbert spaces in terms of general properties of $\mathsf{G}$-Hilbert $\Im$-modules‎. ‎In particular‎, ‎we show that $\mathsf{G}$-Hilbert $\Im$-(bi)modules on $\mathsf{G}$-$C^*$-algebra of compact operators are both projective and injective‎.
 

کلیدواژه‌ها

$G$-projective‎؛ ‎$G$-projective cover‎؛ ‎extremally $G$-disconnected‎؛ ‎$G$-$C^*$-algebra‎؛ ‎$G$-Hilbert $\Im$-module‎؛ ‎$G$-injective Hilbert $\Im$-module‎؛ ‎$G$-projective Hilbert $\Im$-module‎؛ ‎$G$-self dual‎؛ ‎$G$-monotone complete‎؛ ‎$G$-$*$-representation

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