Abstract
This paper is investigative work into the properties of a family of graded algebras recently defined by Varagnolo and Vasserot, which we call VV algebras. We compare categories of modules over KLR algebras with categories of modules over VV algebras, establishing various Morita equivalences. Using these Morita equivalences we are able to prove several properties of certain classes of VV algebras such as (graded) affine cellularity and affine quasi-heredity.
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Acknowledgments
This work makes up part of my PhD thesis which was completed at the University of East Anglia under the supervision of Dr Vanessa Miemietz. I would like to thank Vanessa for all her help, guidance and ideas throughout. I also thank the School of Mathematics and the University of East Anglia for the studentship and the financial support that came with it. This work was submitted whilst at the University of Stuttgart. I would like to thank Prof. Steffen Koenig for allowing me to complete this work in Stuttgart and for many helpful and interesting discussions. Finally, I would like the thank the referees for taking the time to read this paper carefully and for providing a list of helpful comments and suggestions.
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Presented by: Alistair Savage
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Walker, R. On Morita Equivalences Between KLR Algebras and VV Algebras. Algebr Represent Theor 23, 759–794 (2020). https://doi.org/10.1007/s10468-019-09865-9
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DOI: https://doi.org/10.1007/s10468-019-09865-9