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

Abstract

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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.

How to cite

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Heydari, 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

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  2. Frölicher A., Nijenhuis A., Theory of vector valued differential forms, Part I, Indag. Math. 18 (1956), 338–359. (1956) MR0082554
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  6. Manin Z. I., Gauge field theory and complex geometry, Springer-Verlag, Berlin, 1988. (1988) Zbl0641.53001MR0954833
  7. 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
  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. (1988) MR1034284
  9. Nijenhuis A., Richardson R., Cohomoloy and deformations in graded Lie algebras, Bull. Amer. Math. Soc. 72 (1966), 1–29. (1966) MR0195995
  10. Nijenhuis A., Richardson R., Deformation of Lie algebra structres, J. Math. Mech. 17 (1967), 89–105. (1967) MR0214636
  11. Osborn H., Affine connections complexes, Acta Appl. Math. 59 (1999), 215–227. (1999) MR1741659
  12. Poor A. W., Differential geometric structures, McGraw-Hill Company, 1981. (1981) Zbl0493.53027MR0647949

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