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 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 O-algebras whose extension to the quotient field of O is separable.

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Keywords
symmetric algebras, Tate duality, Knörr lattices
Mathematical Subject Classification 2010
Primary: 20C20
Secondary: 16H10
Milestones
Received: 5 April 2017
Revised: 13 September 2017
Accepted: 15 September 2017
Published: 23 November 2017
Authors
Florian Eisele
City University London
London
United Kingdom
Michael Geline
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL
United States
Radha Kessar
City University London
London
United Kingdom
Markus Linckelmann
City University London
London
United Kingdom