A description of derivations of the algebra of symmetric tensors
Archivum mathematicum, Tome 42 (2006) no. 2, pp. 175-184 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 53A55, 53C05, 58A10
Keywords: derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor
@article{ARM_2006_42_2_a8,
     author = {Heydari, A. and Boroojerdian, N. and Peyghan, E.},
     title = {A description of derivations of the algebra of symmetric tensors},
     journal = {Archivum mathematicum},
     pages = {175--184},
     year = {2006},
     volume = {42},
     number = {2},
     mrnumber = {2240355},
     zbl = {1164.53401},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a8/}
}
TY  - JOUR
AU  - Heydari, A.
AU  - Boroojerdian, N.
AU  - Peyghan, E.
TI  - A description of derivations of the algebra of symmetric tensors
JO  - Archivum mathematicum
PY  - 2006
SP  - 175
EP  - 184
VL  - 42
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a8/
LA  - en
ID  - ARM_2006_42_2_a8
ER  - 
%0 Journal Article
%A Heydari, A.
%A Boroojerdian, N.
%A Peyghan, E.
%T A description of derivations of the algebra of symmetric tensors
%J Archivum mathematicum
%D 2006
%P 175-184
%V 42
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a8/
%G en
%F ARM_2006_42_2_a8
Heydari, A.; Boroojerdian, N.; Peyghan, E. A description of derivations of the algebra of symmetric tensors. Archivum mathematicum, Tome 42 (2006) no. 2, pp. 175-184. http://geodesic.mathdoc.fr/item/ARM_2006_42_2_a8/

[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

[2] Frölicher A., Nijenhuis A.: Theory of vector valued differential forms. Part I, Indag. Math. 18 (1956), 338–359. | MR

[3] Greub W., Halperin S., Vanstone R.: Connections, Curvature and Cohomology. Vol 2, Academic Press, 1973. | Zbl

[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

[5] Lewis A. D., Murray R. M.: Controllability of simple mechanical control systems. SIAM J. Control Optim. 35 (3) (1997), 766–790. | MR | Zbl

[6] Manin Z. I.: Gauge field theory and complex geometry. Springer-Verlag, Berlin, 1988. | MR | Zbl

[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

[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

[9] Nijenhuis A., Richardson R.: Cohomoloy and deformations in graded Lie algebras. Bull. Amer. Math. Soc. 72 (1966), 1–29. | MR

[10] Nijenhuis A., Richardson R.: Deformation of Lie algebra structres. J. Math. Mech. 17 (1967), 89–105. | MR

[11] Osborn H.: Affine connections complexes. Acta Appl. Math. 59 (1999), 215–227. | MR

[12] Poor A. W.: Differential geometric structures. McGraw-Hill Company, 1981. | MR | Zbl