Noncommutative Differential Geometry of Generalized Weyl Algebras
Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p;q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p;q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particu...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147755 |
| 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: | Noncommutative Differential Geometry of Generalized Weyl Algebras / T. Brzeziński // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147755 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1477552019-02-16T01:24:16Z Noncommutative Differential Geometry of Generalized Weyl Algebras Brzeziński, T. Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p;q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p;q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p;q) are constructed, and three-dimensional first-order differential calculi induced by these derivations are described. The associated integrals are computed and it is shown that the dimension of the integral space coincides with the order of the defining polynomial p(z). It is proven that the restriction of these first-order differential calculi to the calculi on B(p;q) is isomorphic to the direct sum of degree 2 and degree −2 components of A(p;q). A Dirac operator for B(p;q) is constructed from a (strong) connection with respect to this differential calculus on the (free) spinor bimodule defined as the direct sum of degree 1 and degree −1 components of A(p;q). The real structure of KO-dimension two for this Dirac operator is also described. 2016 Article Noncommutative Differential Geometry of Generalized Weyl Algebras / T. Brzeziński // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16S38; 58B32; 58B34 DOI:10.3842/SIGMA.2016.059 http://dspace.nbuv.gov.ua/handle/123456789/147755 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 |
Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p;q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p;q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p;q) are constructed, and three-dimensional first-order differential calculi induced by these derivations are described. The associated integrals are computed and it is shown that the dimension of the integral space coincides with the order of the defining polynomial p(z). It is proven that the restriction of these first-order differential calculi to the calculi on B(p;q) is isomorphic to the direct sum of degree 2 and degree −2 components of A(p;q). A Dirac operator for B(p;q) is constructed from a (strong) connection with respect to this differential calculus on the (free) spinor bimodule defined as the direct sum of degree 1 and degree −1 components of A(p;q). The real structure of KO-dimension two for this Dirac operator is also described. |
| format |
Article |
| author |
Brzeziński, T. |
| spellingShingle |
Brzeziński, T. Noncommutative Differential Geometry of Generalized Weyl Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Brzeziński, T. |
| author_sort |
Brzeziński, T. |
| title |
Noncommutative Differential Geometry of Generalized Weyl Algebras |
| title_short |
Noncommutative Differential Geometry of Generalized Weyl Algebras |
| title_full |
Noncommutative Differential Geometry of Generalized Weyl Algebras |
| title_fullStr |
Noncommutative Differential Geometry of Generalized Weyl Algebras |
| title_full_unstemmed |
Noncommutative Differential Geometry of Generalized Weyl Algebras |
| title_sort |
noncommutative differential geometry of generalized weyl algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147755 |
| citation_txt |
Noncommutative Differential Geometry of Generalized Weyl Algebras / T. Brzeziński // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT brzezinskit noncommutativedifferentialgeometryofgeneralizedweylalgebras |
| first_indexed |
2023-05-20T17:28:14Z |
| last_indexed |
2023-05-20T17:28:14Z |
| _version_ |
1796153371293384704 |