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Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3
Інший ID:
2010 Mathematics Subject Classification: 15A75; 57Q99; 57R56
DOI: http://dx.doi.org/10.3842/SIGMA.2013.053
DOI: http://dx.doi.org/10.3842/SIGMA.2013.053
Посилання:
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.
Підтримка:
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).
Дата:
2013
Переглядів:
576
Завантажень:
254
Анотація:
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.
