On Tate duality and a projective scalar property for symmetric algebras

Eisele, F. , Geline, M., Kessar, R. and Linckelmann, M. (2018) On Tate duality and a projective scalar property for symmetric algebras. Pacific Journal of Mathematics, 293(2), pp. 277-300. (doi: 10.2140/pjm.2018.293.277)

Abstract

We identify a class of symmetric algebras over a complete discrete valuation ring  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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Eisele, Dr Florian
• Authors: Eisele, F., Geline, M., Kessar, R., and Linckelmann, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Pacific Journal of Mathematics
• Publisher: Mathematical Sciences Publisher
• ISSN: 0030-8730
• ISSN (Online): 0030-8730
• Published Online: 23 November 2017
• Copyright Holders: Copyright © 2018 Mathematical Sciences Publishers
• First Published: First published in Pacific Journal of Mathematics 293(2): 277-300
• Publisher Policy: Reproduced in accordance with the publisher copyright policy