G L n -Invariant tensors and graphs

Martin Markl

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 5, page 449-463
  • ISSN: 0044-8753

Abstract

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We describe a correspondence between GL n -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.

How to cite

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Markl, Martin. "$GL_n$-Invariant tensors and graphs." Archivum Mathematicum 044.5 (2008): 449-463. <http://eudml.org/doc/250506>.

@article{Markl2008,
abstract = {We describe a correspondence between $\mbox\{GL\}_n$-invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.},
author = {Markl, Martin},
journal = {Archivum Mathematicum},
keywords = {invariant tensor; general linear group; graph; invariant tensors; general linear groups; graphs},
language = {eng},
number = {5},
pages = {449-463},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$GL_n$-Invariant tensors and graphs},
url = {http://eudml.org/doc/250506},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Markl, Martin
TI - $GL_n$-Invariant tensors and graphs
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 5
SP - 449
EP - 463
AB - We describe a correspondence between $\mbox{GL}_n$-invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.
LA - eng
KW - invariant tensor; general linear group; graph; invariant tensors; general linear groups; graphs
UR - http://eudml.org/doc/250506
ER -

References

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  2. Kauffman, L. H., Knots and Physics, Series on Knots and Everything , Vol. 1, World Scientific, 1991. (1991) Zbl0733.57004MR1141156
  3. Kolář, I, Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. (1993) MR1202431
  4. Kontsevich, M., Formal (non)commutative symplectic geometry, The Gel'fand mathematics seminars 1990–1992, Birkhäuser, 1993. (1993) Zbl0821.58018MR1247289
  5. Markl, M., Natural differential operators and graph complexes, Preprint math.DG/0612183, December 2006. To appear in Differential Geometry and its Applications. Zbl1165.51005MR2503978
  6. Markl, M., Merkulov, S. A., Shadrin, S., Wheeled PROPs, graph complexes and the master equation, Preprint math.AG/0610683, October 2006. To appear in Journal of Pure and Applied Algebra. MR2483835
  7. Weyl, H., The classical groups. Their invariants and representations. Fifteenth printing, Princeton University Press, 1997. (1997) MR1488158

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