arXiv subjects

Anton Izosimov

Publications and source records attributed to Anton Izosimov.

39 records · Page 3Linked to original sources

arXiv2013

The derived algebra of a stabilizer, families of coadjoint orbits, and sheets

Let $\mathfrak{g}$ be a finite-dimensional real or complex Lie algebra, and let $μ\in \mathfrak{g}^{*}$. In the first part of the paper, the relation is discussed between the derived algebra of the stabilizer of $μ$ and the set of coadjoint orbits which have the same dimension as the orbit of $μ$. In the second part, semisimple Lie algebras are considered, and the relation is discussed between the derived algebra of a centralizer and sheets.

math.RT↗

arXiv2013

Singularities of bi-Hamiltonian systems

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degeneracy of singular points of bi-Hamiltonian systems and describe their types.

math-ph↗

arXiv2012

A note on relative equilibria of multidimensional rigid body

It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a multidimensional body: a rotation is stationary if and only if it is a rotation in the principal axes of inertia, provided that the eigenvalues of the angular velocity matrix are pairwise distinct. However, if some eigenvalues of the angular velocity matrix of a stationary rotation coincide, then it is possible that this rotation has a different nature. A description of such rotations is given in the present paper.

math-ph↗