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POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS
Glasgow Mathematical Journal ( IF 0.548 ) Pub Date : 2019-10-02 , DOI: 10.1017/s0017089519000429
DAVID KYED; HENRIK DENSING PETERSEN

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.
更新日期:2019-10-02

 

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