Lie theory of multiplicative tensors

Arithmetic Deformation Theory of Lie Algebras

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...

Multiplicative Dirac structures on Lie groups

We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space inherits the structure of a Poisson-Lie group. We also describe multiplicative Dirac structures on Lie groups infinitesimally. Résumé Nous étudions les structure...

Approximate Multiplicative Groups in Nilpotent Lie Groups

We generalize a result of Tao which describes approximate multiplicative groups in the Heisenberg group. We extend it to simply connected nilpotent Lie groups of arbitrary step.

Tropical Spectral Theory of Tensors

We introduce and study tropical eigenpairs of tensors, a generalization of the tropical spectral theory of matrices. We show the existence and uniqueness of an eigenvalue. We associate to a tensor a directed hypergraph and define a new type of cycle on a hypergraph, which we call an H-cycle. The eigenvalue of a tensor turns out to be equal to the minimal normalized weighted length of H-cycles o...

Multiplicative Ideal Theory