POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS

@article{Kyed2019POLYNOMIALCA,
  title={POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS},
  author={David Kyed and Henrik DENSING PETERSEN},
  journal={Glasgow Mathematical Journal},
  year={2019},
  volume={62},
  pages={706 - 736}
}
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… Expand
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References

SHOWING 1-10 OF 56 REFERENCES
On the cohomology of weakly almost periodic group representations
We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using theExpand
Polynomial mappings of groups
A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsDh,h ∈G, defined byDhϕ(g)=ϕ(g)−1ϕ(gh). We study polynomial mappingsExpand
Orbit equivalence rigidity and bounded cohomology
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wideExpand
Continuous Bounded Cohomology of Locally Compact Groups
The purpose of this monograph is (a) to lay the foundations for a conceptual approach to bounded cohomology; (b) to harvest the resulting applications in rigidity theory. Of central importance is theExpand
Integrable measure equivalence for groups of polynomial growth
Bader, Furman and Sauer have introduced the notion of integrable measure equivalence for finitely-generated groups. This is the sub-equivalence relation of measure equivalence obtained by insistingExpand
Asymptotic cones of Lie groups and cone equivalences
We introduce cone bilipschitz equivalences between metric spaces. These are maps, more general than quasi-isometries, that induce a bilipschitz homeomorphism between asymptotic cones. Non-trivialExpand
The lower central series of the free partially commutative group
This paper is devoted to the study of the lower central series of the free partially commutative groupF(A, ϑ) in connection with the associated free partially commutative Lie algebra. Using aExpand
Lecture notes on nilpotent groups
An algebraic prelude Continuity of automorphisms and derivations $C^*$-algebra axiomatics and basic results Derivations of $C^*$-algebras Homogeneous $C^*$-algebras CCR-algebras $W^*$ andExpand
ON POLYNOMIAL FUNCTORS
Polynomial functors appeared in algebraic topology [8] and proved themselves useful in various questions of this theory, especially in studying homotopy types. So their classification is of aExpand
An Introduction to Lie Groups and Lie Algebras
With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch ofExpand
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