Geodesic
POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS
Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 706-736

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DOI

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. 
KYED, DAVID; PETERSEN, HENRIK DENSING. POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS. Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 706-736. doi: 10.1017/S0017089519000429
@article{10_1017_S0017089519000429,
     author = {KYED, DAVID and PETERSEN, HENRIK DENSING},
     title = {POLYNOMIAL {COHOMOLOGY} {AND} {POLYNOMIAL} {MAPS} {ON} {NILPOTENT} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {706--736},
     year = {2020},
     volume = {62},
     number = {3},
     doi = {10.1017/S0017089519000429},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000429/}
}
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%D 2020
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