Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3
We consider relations in Grassmann algebra corresponding to the four-dimensional Pachner move 3-3, assuming that there is just one Grassmann variable on each 3-face, and a 4-simplex weight is a Grassmann-Gaussian exponent depending on these variables on its five 3-faces. We show that there exists a...
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Інститут математики НАН України
2013
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149347 |
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| Zitieren: | Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 / I.G. Korepanov, N.M. Sadykov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1493472025-02-09T12:22:29Z Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 Korepanov, I.G. Sadykov, N.M. We consider relations in Grassmann algebra corresponding to the four-dimensional Pachner move 3-3, assuming that there is just one Grassmann variable on each 3-face, and a 4-simplex weight is a Grassmann-Gaussian exponent depending on these variables on its five 3-faces. We show that there exists a large family of such relations; the problem is in finding their algebraic-topologically meaningful parameterization. We solve this problem in part, providing two nicely parameterized subfamilies of such relations. For the second of them, we further investigate the nature of some of its parameters: they turn out to correspond to an exotic analogue of middle homologies. In passing, we also provide the 2-4 Pachner move relation for this second case. We thank the creators and maintainers of GAP2 and Maxima3 for their excellent computer algebra systems. We also thank the referees for valuable comments, including drawing our attention to the literature on holonomic functions (see Remark 3). 2013 Article Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 / I.G. Korepanov, N.M. Sadykov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 15A75; 57Q99; 57R56 DOI: http://dx.doi.org/10.3842/SIGMA.2013.053 https://nasplib.isofts.kiev.ua/handle/123456789/149347 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider relations in Grassmann algebra corresponding to the four-dimensional Pachner move 3-3, assuming that there is just one Grassmann variable on each 3-face, and a 4-simplex weight is a Grassmann-Gaussian exponent depending on these variables on its five 3-faces. We show that there exists a large family of such relations; the problem is in finding their algebraic-topologically meaningful parameterization. We solve this problem in part, providing two nicely parameterized subfamilies of such relations. For the second of them, we further investigate the nature of some of its parameters: they turn out to correspond to an exotic analogue of middle homologies. In passing, we also provide the 2-4 Pachner move relation for this second case. |
| format |
Article |
| author |
Korepanov, I.G. Sadykov, N.M. |
| spellingShingle |
Korepanov, I.G. Sadykov, N.M. Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Korepanov, I.G. Sadykov, N.M. |
| author_sort |
Korepanov, I.G. |
| title |
Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 |
| title_short |
Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 |
| title_full |
Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 |
| title_fullStr |
Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 |
| title_full_unstemmed |
Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 |
| title_sort |
parameterizing the simplest grassmann-gaussian relations for pachner move 3-3 |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149347 |
| citation_txt |
Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 / I.G. Korepanov, N.M. Sadykov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 13 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT korepanovig parameterizingthesimplestgrassmanngaussianrelationsforpachnermove33 AT sadykovnm parameterizingthesimplestgrassmanngaussianrelationsforpachnermove33 |
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2025-11-25T23:46:47Z |
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2025-11-25T23:46:47Z |
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