Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic computer calculations; their essential new feature is th...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148082 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148082 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1480822019-02-17T01:25:10Z Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves Korepanov, I.G. New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic computer calculations; their essential new feature is that, although they can be treated as deformations of relations corresponding to torsions of acyclic complexes, they can no longer be explained in such terms. In the simpler case of three dimensions, we define an invariant, based on our relations, of a piecewise-linear manifold with triangulated boundary, and present example calculations confirming its nontriviality. 2011 Article Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 15A75; 55-04; 57M27, 57Q10; 57R56 DOI: http://dx.doi.org/10.3842/SIGMA.2011.117 http://dspace.nbuv.gov.ua/handle/123456789/148082 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic computer calculations; their essential new feature is that, although they can be treated as deformations of relations corresponding to torsions of acyclic complexes, they can no longer be explained in such terms. In the simpler case of three dimensions, we define an invariant, based on our relations, of a piecewise-linear manifold with triangulated boundary, and present example calculations confirming its nontriviality. |
| format |
Article |
| author |
Korepanov, I.G. |
| spellingShingle |
Korepanov, I.G. Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Korepanov, I.G. |
| author_sort |
Korepanov, I.G. |
| title |
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_short |
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_full |
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_fullStr |
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_full_unstemmed |
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_sort |
relations in grassmann algebra corresponding to three- and four-dimensional pachner moves |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148082 |
| citation_txt |
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT korepanovig relationsingrassmannalgebracorrespondingtothreeandfourdimensionalpachnermoves |
| first_indexed |
2023-05-20T17:29:14Z |
| last_indexed |
2023-05-20T17:29:14Z |
| _version_ |
1796153406034804736 |