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oai:figshare.com:article/32631789 2026-10-01T17:16:47Z portal_1172 item_type_8 month_year_10_2026

Cohomological dimension for C*-algebras Michael Rosbotham (24164631) PUREID: 250429787 Operator module C*-algebra exact category dimension homological algebra cohomology operator space We define and explore invariants for C*-algebras that arise as cohomological dimensions for associated categories of operator space modules. The setting of exact categories provides us with a robust framework to utilise homological techniques.<br><br>We develop initial global dimension theorems for two of these categories. In the additive category of operator modules over a C*-algebra, equipped with the exact structure of all kernel-cokernel pairs, we show how an extension theorem of Wittstock and a representation theorem of Christensen-Effros-Sinclair can be used to build injective resolutions. From there, we establish a lower bound for the associated global dimension.<br><br>We also investigate the sub–exact structure of kernel-cokernel pairs that split as completely bounded linear maps. This provides a new context in which to discuss relative homological algebra for operator modules over a C*-algebra. We provide a proof that the cohomological dimension of this exact category is zero ifand only if the C*-algebra is classically semisimple. 2026-10-01T17:16:47Z Text Thesis 10.17034/32631789.v1 https://figshare.com/articles/thesis/Cohomological_dimension_for_C_-algebras/32631789 All Rights Reserved