Work in progress

Preprints and publications

• A. Verbovetsky, Remarks on two approaches to the horizontal cohomology: compatibility complex and the Koszul-Tate resolution, Preprint ESI (in preparation).
• I. S. Krasil'shchik and A. Verbovetsky, Homological methods in equations of mathematical physics, Open Education and Sciences, Opava, 1998, Report no. DIPS 7/98, E-print math.DG/9808130 (Russian translation will be published by the Independent University of Moscow).
• A. Verbovetsky, Notes on the horizontal cohomology, Secondary Calculus and Cohomological Physics (M. Henneaux, I. S. Krasil'shchik, and A. M. Vinogradov, eds.), Contemporary Mathematics, Amer. Math. Soc., Providence, R.I., 1998, pp. 211-231, Report no. DIPS 3/98, E-print math.DG/9803115.
• A. Verbovetsky, On the cohomology of the compatibilitycomplex, Uspekhi Mat. Nauk, 53 (1998), no. 1,213-214 (Russian); English translation in Russian Math. Surveys53 (1998), no. 1, 225-226.
• A. M. Verbovetsky, On super Lagrangian systems andtheir generalizations, Ph.D. thesis, Moscow State Univ.,1998 (Russian).
• A. Verbovetsky, On quantized algebra of Wess-Zuminodifferential operators at roots of unity, Acta Appl. Math.,49 (1997), 363-370, Report no. SISSA 66/95/FM,DIPS 5/96,E-print q-alg/9505005.
• A. Verbovetsky, Differential operators over quantumspaces, Acta Appl. Math., 49 (1997), 339-361,Report no. SISSA 69/95/FM, DIPS 4/96.
• A. V. Bocharov,V. N. Chetverikov,S. V. Duzhin,N. G. Khor'kova,I. S. Krasil'shchik,A. V. Samokhin,Yu. N. Torkhov,A. M. Verbovetsky,and A. M. Vinogradov,Symmetries and conservation laws for differential equations ofmathematical physics, Monograph(I. S. Krasil'shchik andA. M.Vinogradov, eds.),Faktorial Publ., 1997 (Russian); English transl.: Amer. Math. Soc.,Providence, R.I., Translations of mathematical monographs,vol. 182, 1999.
• A. Verbovetsky, Lagrangian formalism over graded algebras,J. Geom. Phys., 18 (1996), 195-214, Report no. SISSA 93/94/FM,E-print hep-th/9407037.
• N. G. Khor'kova andA. M. Verbovetsky, On symmetry subalgebras and conservationlaws for the k-e turbulence model and the Navier- Stokes equations,The Interplay between Differential Geometry and Differential Equations(V. V. Lychagin, ed.), Amer. Math. Soc. Transl.(2),vol. 167, Amer. Math. Soc., Providence,R.I., 1995, pp. 61-90.
• A. M. Verbovetsky, A. M. Vinogradov, D. M. Gessler,Scalar differential invariants and characteristic classes ofhomogeneous geometric structures, Mat. Zametki, 51 (1992),no. 6, 15-26 (Russian); English translation in Math. Notes, 51(1992), 543-549.
• A. M. Verbovetsky, Local nonintegrability of long-shotwave interaction equations, Acta Appl. Math., 15 (1989),121-136.