# A description of derivations of the algebra of symmetric tensors

A. Heydari; N. Boroojerdian; E. Peyghan

Archivum Mathematicum (2006)

- Volume: 042, Issue: 2, page 175-184
- ISSN: 0044-8753

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topHeydari, A., Boroojerdian, N., and Peyghan, E.. "A description of derivations of the algebra of symmetric tensors." Archivum Mathematicum 042.2 (2006): 175-184. <http://eudml.org/doc/249832>.

@article{Heydari2006,

abstract = {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.},

author = {Heydari, A., Boroojerdian, N., Peyghan, E.},

journal = {Archivum Mathematicum},

keywords = {derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor; derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor},

language = {eng},

number = {2},

pages = {175-184},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {A description of derivations of the algebra of symmetric tensors},

url = {http://eudml.org/doc/249832},

volume = {042},

year = {2006},

}

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

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 2

SP - 175

EP - 184

AB - 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.

LA - eng

KW - derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor; derivation; Frölicher-Nijenhius bracket; symmetric differential; symmetric Lie derivative; symmetric tensor

UR - http://eudml.org/doc/249832

ER -

## References

top- Crouch P. E., Geometric structures in systems theory, Institution of Electrical Engineers. Proccedings D. Control Theory and Applications 128(5) (1981), 242–252. (1981) MR0631984
- Frölicher A., Nijenhuis A., Theory of vector valued differential forms, Part I, Indag. Math. 18 (1956), 338–359. (1956) MR0082554
- Greub W., Halperin S., Vanstone R., Connections, Curvature and Cohomology, Vol 2, Academic Press, 1973. (1973) Zbl0335.57001
- 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. (1980) MR0575212
- Lewis A. D., Murray R. M., Controllability of simple mechanical control systems, SIAM J. Control Optim. 35 (3) (1997), 766–790. (1997) Zbl0870.53013MR1444338
- Manin Z. I., Gauge field theory and complex geometry, Springer-Verlag, Berlin, 1988. (1988) Zbl0641.53001MR0954833
- Michor P. W., Remarks on the Frölicher-Nijenhuis bracket, Proccedings of the Conference on Differential Geometry and its Applications, Brno (1986), 197–220. (1986) MR0923350
- 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. (1988) MR1034284
- Nijenhuis A., Richardson R., Cohomoloy and deformations in graded Lie algebras, Bull. Amer. Math. Soc. 72 (1966), 1–29. (1966) MR0195995
- Nijenhuis A., Richardson R., Deformation of Lie algebra structres, J. Math. Mech. 17 (1967), 89–105. (1967) MR0214636
- Osborn H., Affine connections complexes, Acta Appl. Math. 59 (1999), 215–227. (1999) MR1741659
- Poor A. W., Differential geometric structures, McGraw-Hill Company, 1981. (1981) Zbl0493.53027MR0647949

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