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Poincaré duality in modular coinvariant rings


Authors: Müfit Sezer and Wenliang Zhang
Journal: Proc. Amer. Math. Soc. 144 (2016), 5113-5120
MSC (2010): Primary 13A50
DOI: https://doi.org/10.1090/proc/13245
Published electronically: July 21, 2016
MathSciNet review: 3556257
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Abstract: We classify the modular representations of a cyclic group of prime order whose corresponding rings of coinvariants are Poincaré duality algebras. It turns out that these algebras are actually complete intersections. For other representations we demonstrate that the dimension of the top degree of the coinvariants grows at least linearly with respect to the number of summands of dimension at least four in the representation.


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Additional Information

Müfit Sezer
Affiliation: Department of Mathematics, Bilkent University, Ankara, 06800, Turkey
Email: sezer@fen.bilkent.edu.tr

Wenliang Zhang
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, Illinois 60607
Email: wlzhang@uic.edu

DOI: https://doi.org/10.1090/proc/13245
Received by editor(s): May 26, 2015
Received by editor(s) in revised form: February 22, 2016
Published electronically: July 21, 2016
Additional Notes: The first author was supported by a grant from Tübitak:114F427
The second author was partially supported by NSF grants DMS #1247354, #1405602
Communicated by: Harm Derksen
Article copyright: © Copyright 2016 American Mathematical Society