Polynomial Cohomology and Polynomial Maps on Nilpotent Groups

David Kyed*, Henrik Densing Petersen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We introduce a refined version of group cohomology and relate it to the space of polynomials on the group in question. We show that the polynomial cohomology with trivial coefficients admits a description in terms of ordinary cohomology with polynomial coefficients, and that the degree one polynomial cohomology with trivial coefficients admits a description directly in terms of polynomials. Lastly, we give a complete description of the polynomials on a connected, simply connected nilpotent Lie group by showing that these are exactly the maps that pull back to classical polynomials via the exponential map.
Translated title of the contributionPolynomial Cohomology and Polynomial Maps on Nilpotent Groups
Original languageEnglish
JournalGlasgow Mathematical Journal
Volume62
Issue number3
Pages (from-to)706-736
ISSN0017-0895
DOIs
Publication statusPublished - Sept 2020

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