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High Quality Content by WIKIPEDIA articles! In mathematics, Tannaka Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. Its natural extension to the non-Abelian case is the Grothendieck duality theory. It extends an important mathematical duality between compact and discrete commutative topological groups, known as Pontryagin duality, to groups that are compact, but noncommutative. The theory is named for two men, the Soviet mathematician Mark Grigorievich Krein, and the Japanese Tadao Tannaka. In contrast to the case of…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, Tannaka Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. Its natural extension to the non-Abelian case is the Grothendieck duality theory. It extends an important mathematical duality between compact and discrete commutative topological groups, known as Pontryagin duality, to groups that are compact, but noncommutative. The theory is named for two men, the Soviet mathematician Mark Grigorievich Krein, and the Japanese Tadao Tannaka. In contrast to the case of commutative groups considered by Lev Pontryagin, the notion dual to a noncommutative compact group is not a group, but a category (G) with some additional structures, formed by the finite-dimensional representations of G.