Karmazyn, J. orcid.org/0000-0003-4518-0044 (2014) Superpotentials, Calabi-Yau algebras, and PBW deformations. Journal of Pure and Applied Algebra, 413. pp. 100-134. ISSN 0022-4049
Abstract
The paper [9] by Bocklandt, Schedler and Wemyss considers path algebras with relations given by the higher derivations of a superpotential, giving a condition for such an algebra to be Calabi–Yau. In particular they show that the algebra , for V a finite dimensional vector space and G a finite subgroup of , is Morita equivalent to a path algebra with relations given by a superpotential, and is Calabi–Yau for
. In this paper we extend these results, giving a condition for a PBW deformation of a Calabi–Yau, Koszul path algebra with relations given by a superpotential to have relations given by a superpotential, and proving these are Calabi–Yau in certain cases.
We apply our methods to symplectic reflection algebras, where we show that every symplectic reflection algebra is Morita equivalent to a path algebra whose relations are given by the higher derivations of an inhomogeneous superpotential. In particular we show these are Calabi–Yau regardless of the deformation parameter.
Also, for G a finite subgroup of not contained in , we consider PBW deformations of a path algebra with relations which is Morita equivalent to . We show there are no non-trivial PBW deformations when G is a small subgroup.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2014 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/) |
Keywords: | Path algebra; Superpotential; Calabi–Yau algebras; Koszul algebras; PBW deformations |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Oct 2017 08:23 |
Last Modified: | 22 Feb 2018 15:45 |
Published Version: | https://doi.org/10.1016/j.jalgebra.2014.05.007 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jalgebra.2014.05.007 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:122054 |