Study some properties of reflexive and dihedral homology on operator algebras | ||||
| Aswan Science and Technology Bulletin | ||||
| Articles in Press, Corrected Proof, Available Online from 07 September 2025 PDF (609.38 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/astb.2025.387609.1024 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
A. H. NORELDEEN 1; Hegagi Ali2; Aya Ahmed  3; Faten Ragab Karar4
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| 1Department of Mathematics, Faculty of Science, Aswan University, Aswa, Egypt. | ||||
| 2Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt | ||||
| 3Department of Basic and Applied Sciences, Arab Academy for Science, Technology & Maritime Transport, Aswan, Egypt. | ||||
| 4Mathematics department ,faculty of science, Aswan University | ||||
| Abstract | ||||
| The homology properties of Banach algebras have been a central topic in functional analysis, with foundational contributions by Johnson, Kadison, Sinclair, and Ringrose leading to classifications based on Hochschild (co)homology and the concept of amenability. The interplay between Hochschild, cyclic, and dihedral (co)homology has further enriched the study of Banach and operator algebras, with key developments in biflatness, bi-projectivity, and ideal amenability. Recent research has focused on the computation of dihedral homology for Banach algebras, utilizing projective tensor powers and Hochschild complexes. By extending classical homological tools, we introduce a framework for relative reflexive homology and analyze its properties within involutive Banach algebras. Furthermore, we construct free involutive resolutions and explore their role in the homological classification of Banach algebras. There are many applications in the general sciences. Our results establish fundamental connections between dihedral homology, cyclic homology, and reflexive homology, which offer new perspectives on the algebraic and functional structure of Banach algebras and operator algebras. | ||||
| Keywords | ||||
| Dihedral Homology; Complexes; Exact Sequence; Operator Algebra; Reflexive Homology | ||||
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