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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149347 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862563999835488256 |
|---|---|
| author | Korepanov, I.G. Sadykov, N.M. |
| author_facet | Korepanov, I.G. Sadykov, N.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T23:46:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149347 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T23:46:47Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Korepanov, I.G. Sadykov, N.M. 2019-02-21T07:06:26Z 2019-02-21T07:06:26Z 2013 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 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). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 Article published earlier |
| spellingShingle | Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 Korepanov, I.G. Sadykov, N.M. |
| title | 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_short | Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3 |
| title_sort | parameterizing the simplest grassmann-gaussian relations for pachner move 3-3 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149347 |
| work_keys_str_mv | AT korepanovig parameterizingthesimplestgrassmanngaussianrelationsforpachnermove33 AT sadykovnm parameterizingthesimplestgrassmanngaussianrelationsforpachnermove33 |