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 $\mathcal{O}$ 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 $\mathcal{O}$-algebras whose extension to the quotient field of $\mathcal{O}$ is separable.

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