Structure of the unitary valuation algebra

Fu, Joseph H.G.

Fu, Joseph H.G.

J. Differential Geom., Tome 72 (2006) no. 1, p. 509-533 / Harvested from Project Euclid

Résumé

S. Alesker has shown that if G is a compact subgroup of O(n) acting transitively on the unit sphere S^n-1, then the vector space Val^G of continuous, translation-invariant, G-invariant convex valuations on Rⁿ has the structure of a finite dimensional graded algebra over R satisfying Poincaré duality. We show that the kinematic formulas for G are determined by the product pairing. Using this result we then show that the algebra Val^U(n) is isomorphic to R[s, t]/(f_n+1, f_n+2), where s, t have degrees 2 and 1 respectively, and the polynomial f_i is the degree i term of the power series log(1 + s + t).

Publié le : 2006-03-14
Classification:

@article{1143593748,
     author = {Fu, Joseph H.G.},
     title = {Structure of the unitary valuation algebra},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 509-533},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1143593748}
}

Fu, Joseph H.G. Structure of the unitary valuation algebra. J. Differential Geom., Tome 72 (2006) no. 1, pp.  509-533. http://gdmltest.u-ga.fr/item/1143593748/