Geodesic
A matrix solution of the pentagon equation with anticommuting variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 3, pp. 513-528 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct a solution of the pentagon equation with anticommuting variables on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are assigned to tetrahedron vertices. Because matrix multiplication is noncommutative, this provides a “more quantum” topological field theory than in our previous works.
Keywords: pentagon equation, topological quantum field theory, algebraic complex
Mots-clés : torsion. 
@article{TMF_2010_163_3_a14,
     author = {S. I. Bel'kov and I. G. Korepanov},
     title = {A~matrix solution of the~pentagon equation with anticommuting variables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {513--528},
     year = {2010},
     volume = {163},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a14/}
}
TY  - JOUR
AU  - S. I. Bel'kov
AU  - I. G. Korepanov
TI  - A matrix solution of the pentagon equation with anticommuting variables
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 513
EP  - 528
VL  - 163
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a14/
LA  - ru
ID  - TMF_2010_163_3_a14
ER  - 
%0 Journal Article
%A S. I. Bel'kov
%A I. G. Korepanov
%T A matrix solution of the pentagon equation with anticommuting variables
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 513-528
%V 163
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a14/
%G ru
%F TMF_2010_163_3_a14
S. I. Bel'kov; I. G. Korepanov. A matrix solution of the pentagon equation with anticommuting variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 3, pp. 513-528. http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a14/

[1] U. Pachner, European. J. Combin., 12:2 (1991), 129–145 | DOI | MR | Zbl

[2] W. B. R. Lickorish, “Simplicial moves on complexes and manifolds”, Proceedings of the Kirbyfest, Geom. Topol. Monogr., 2, eds. J. Hass, M. Scharlemann, Geom. Topol. Publ., Coventry, 1999, 299–320 | DOI | MR | Zbl

[3] E. Moise, Ann. Math. (2), 56:1 (1952), 96–114 | DOI | MR | Zbl

[4] S. I. Bel'kov, I. G. Korepanov, E. V. Martyushev, A simple topological quantum field theory for manifolds with triangulated boundary, arXiv: 0907.3787

[5] I. G. Korepanov, J. Nonlinear Math. Phys., 8:2 (2001), 196–210 | DOI | MR | Zbl

[6] I. G. Korepanov, TMF, 158:1 (2009), 98–114 | DOI | MR | Zbl

[7] I. G. Korepanov, TMF, 158:3 (2009), 405–418 | DOI | MR | Zbl

[8] E. V. Martyushev, Chastnoe soobschenie, 2008

[9] E. V. Martyushev, Izv. Chelyabinsk. nauchn. tsentra, 2003, no. 2(19), 1–5 | MR

[10] E. V. Martyushev, Izv. Chelyabinsk. nauchn. tsentra, 2004, no. 4(26), 1–5 | MR

[11] F. A. Berezin, Vvedenie v algebru i analiz s antikommutiruyuschimi peremennymi, Izd. MGU, M., 1983 | MR

[12] V. G. Turaev, Vvedenie v kombinatornye krucheniya, MTsNMO, M., 2004 | MR | Zbl