Vol. 293, No. 2, 2018

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On Tate duality and a projective scalar property for symmetric algebras

Florian Eisele, Michael Geline, Radha Kessar and Markus Linckelmann

Vol. 293 (2018), No. 2, 277–300
DOI: 10.2140/pjm.2018.293.277
Abstract

We identify a class of symmetric algebras over a complete discrete valuation ring $\mathsc{O}$ of characteristic zero to which the characterisation of Knörr lattices in terms of stable endomorphism rings in the case of finite group algebras can be extended. This class includes finite group algebras, their blocks and source algebras and Hopf orders. We also show that certain arithmetic properties of finite group representations extend to this class of algebras. Our results are based on an explicit description of Tate duality for lattices over symmetric $\mathsc{O}$-algebras whose extension to the quotient field of $\mathsc{O}$ is separable.

Keywords
symmetric algebras, Tate duality, Knörr lattices
Primary: 20C20
Secondary: 16H10