This paper is a continuation of Reduction Modulo 2 and 3 of Euclidean Lattices ([7], Journal of Algebra, 2002). Résumé. Reduction modulo 2 et 3 des réseaux euclidiens (II). Cet article fait suite à l’article [7] Reduction Modulo 2 and 3 of Euclidean Lattices, paru en 2002 au Journal of Algebra.

It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the implementation are derived from scratc...

Some decompositions of the three-dimensional sphere and three-dimensional ball into Jordan curves are considered. In particular, it is proved that for every strictly positive real number p ≤ 1 there exists a partition of the unit three-dimensional Euclidean sphere into circles whose radii are equal to p. Let S2 be the unit two-dimensional sphere in the Euclidean space R3 and let S3 be the unit ...

We show that, if there exists a realization of a Hopf algebra H in a H-module algebra A, then one can split their cross-product into the tensor product algebra of A itself with a subalgebra isomorphic to H and commuting with A. This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean ones, which are obtained as cross-products of the quantum Euc...