$GL_n$-Invariant tensors and graphs
Markl, Martin
Archivum Mathematicum, Tome 044 (2008), p. 449-463 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2008-01-01
Classification:  13A50,  15A72,  20G05
@article{127128,
     author = {Martin Markl},
     title = {$GL\_n$-Invariant tensors and graphs},
     journal = {Archivum Mathematicum},
     volume = {044},
     year = {2008},
     pages = {449-463},
     zbl = {1212.15051},
     mrnumber = {2501578},
     language = {en},
     url = {http://dml.mathdoc.fr/item/127128}
}
Markl, Martin. $GL_n$-Invariant tensors and graphs. Archivum Mathematicum, Tome 044 (2008) pp. 449-463. http://gdmltest.u-ga.fr/item/127128/

Fuks, D. B. Cohomology of infinite dimensional Lie algebras. (Kogomologii beskonechnomernykh algebr Li), Kogomologii beskonechnomernykh algebr Li), Nauka, Moskva, 1984. (1984) | MR 0772201 | Zbl 0592.17011

Kauffman, L. H. Knots and Physics, Series on Knots and Everything , Vol. 1, World Scientific, 1991. (1991) | MR 1141156 | Zbl 0733.57004

Kolář, I; Michor, P. W.; Slovák, J. Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. (1993) | MR 1202431

Kontsevich, M. Formal (non)commutative symplectic geometry, The Gel'fand mathematics seminars 1990–1992, Birkhäuser, 1993. (1993) | MR 1247289 | Zbl 0821.58018

Markl, M. Natural differential operators and graph complexes, Preprint math.DG/0612183, December 2006. To appear in Differential Geometry and its Applications. | MR 2503978 | Zbl 1165.51005

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. | MR 2483835

Weyl, H. The classical groups. Their invariants and representations. Fifteenth printing, Princeton University Press, 1997. (1997) | MR 1488158