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 contribution | Polynomial Cohomology and Polynomial Maps on Nilpotent Groups |
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Original language | English |
Journal | Glasgow Mathematical Journal |
Volume | 62 |
Issue number | 3 |
Pages (from-to) | 706-736 |
ISSN | 0017-0895 |
DOIs | |
Publication status | Published - Sept 2020 |