FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 265-273

**Characteristics of pairs of operators, Lie hybrids, Poisson brackets
and nonlinear geometric algebra**

D. V. Juriev

Abstract

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The article is devoted to various algebraic, geometric and
geometroalgebraic structures, which appear in the context of
the problem of description of pairs of linear operators.
The relations between the problem and investigations of
I. Batalin, A. Weinstein, M. V. Karasev and
V. P. Maslov on the analogs of Lie theory for nonlinear
Poisson brackets, L. V. Sabinin's program of
the nonlinear geometric algebra and the infinite-dimensional
symplectic geometry are explicated.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k001/k00121h.htm

Last modified: April 11, 2000