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.
```

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Location: http://mech.math.msu.su/~fpm/eng/k00/k001/k00121t.htm

Last modified: April 11, 2000