Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 14 1 2021 01 01 Schneider-Teitelbaum duality for locally profinite groups 119 166 87524 10.29252/cgasa.14.1.119 EN Tomoki Mihara University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 Japan Journal Article 2020 06 26 We define monoidal structures on several categories of linear topological modules over the valuation ring of a local field, and study module theory with respect to the monoidal structures. We extend the notion of the Iwasawa algebra to a locally profinite group as a monoid with respect to one of the monoidal structure, which does not necessarily form a topological algebra. This is one of the main reasons why we need monoidal structures. We extend Schneider--Teitelbaum duality to duality applicable to a locally profinite group through the module theory over the generalised Iwasawa algebra, and give a criterion of the irreducibility of a unitary Banach representation. https://cgasa.sbu.ac.ir/article_87524_527d10c49a0e170c47b750c5c9dd850a.pdf