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Keywords:
derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor
derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor
Summary:
In this paper the symmetric differential and symmetric Lie derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frölicher-Nijenhuis bracket for vector valued symmetric tensors.
References:
[1] Crouch P. E.: Geometric structures in systems theory. Institution of Electrical Engineers. Proccedings D. Control Theory and Applications 128(5) (1981), 242–252. MR 0631984
[2] Frölicher A., Nijenhuis A.: Theory of vector valued differential forms. Part I, Indag. Math. 18 (1956), 338–359. MR 0082554
[3] Greub W., Halperin S., Vanstone R.: Connections, Curvature and Cohomology. Vol 2, Academic Press, 1973. Zbl 0335.57001
[4] Grozman P.: Classification of bilinear invariant operators on tensor fields. (Russian) Funct. Anal. Appl. 14, No.2 (1980) 58–59; English translation: Funct. Anal. Appl. 14, No. 2 (1980), 127–128. MR 0575212
[5] Lewis A. D., Murray R. M.: Controllability of simple mechanical control systems. SIAM J. Control Optim. 35 (3) (1997), 766–790. MR 1444338 | Zbl 0870.53013
[6] Manin Z. I.: Gauge field theory and complex geometry. Springer-Verlag, Berlin, 1988. MR 0954833 | Zbl 0641.53001
[7] Michor P. W.: Remarks on the Frölicher-Nijenhuis bracket. Proccedings of the Conference on Differential Geometry and its Applications, Brno (1986), 197–220. MR 0923350
[8] Michor P. W.: Graded derivations of the algebra of differential forms associated with a connection. Proccedings of the Conference on Differential Geometry and its Applications, Peniscola (1988), Springer Lecture Notes in Mathematics, Vol. 1410 (1989), 249–261. MR 1034284
[9] Nijenhuis A., Richardson R.: Cohomoloy and deformations in graded Lie algebras. Bull. Amer. Math. Soc. 72 (1966), 1–29. MR 0195995
[10] Nijenhuis A., Richardson R.: Deformation of Lie algebra structres. J. Math. Mech. 17 (1967), 89–105. MR 0214636
[11] Osborn H.: Affine connections complexes. Acta Appl. Math. 59 (1999), 215–227. MR 1741659
[12] Poor A. W.: Differential geometric structures. McGraw-Hill Company, 1981. MR 0647949 | Zbl 0493.53027
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