**The International Conference on
**

Secondary Calculus and Cohomological Physics,

Moscow, August 24 - August 31, 1997

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Cohomological aspects of Noether theorem for Lagrangians of classical mechanics

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O.M. Khudaverdian, D.A. Sahakyan

Laboratory of Computing Technique and Automation, Joint Institute for Nuclear Research Dubna, Moscow Region 141980, Russia, on leave of absence from Department of Theoretical Physics of Yerevan State University, 375049 Yerevan, Armenia E-mail: khudian@vxjinr.jinr.ru, khudian@sc2a.unige.ch Department of Theoretical Physics, Yerevan State University and University Centre at Joint Institute for Nuclear Research E-mail: sahakian@uniphi.yerphi.am

**Abstract:** For a given configuration space $M$ and Lie algebra ${\G}$ whose action is defined on $M$ the space $\V_{0.0}$ of weakly ${\G}$-invariant Lagrangians (i.e. Lagrangians whose motion equations left hand sides are ${\G}$-invariant) is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex using the method of spectral sequences we arrive at the hierarchy in the space $\V_{0.0}$ corresponding to the cohomologies of the algebra $\G$ and configuration space $M$.

**Full text of the article:**

**Originally archived full text:**

**Nota bene:** The originally archived full text was mistakenly prepared from the TeX source of a different article by the authors, entitled "Double complexes and cohomological hierarchy in a space of weakly invariant Lagrangians of mechanics", of which an extended version appeared in Acta Appl. Math. 56, No. 2, 181-215 (1999). Neither the wrong nor the correct version appeared in the printed version which was published in 1998 as Volume 219 of the AMS series "Contemporary Mathematics" (ISBN 0-8218-0828-1).

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*Publication date for the original electronic files: 22 Dec 1998.
Last modified: 11 Aug 2000.

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