Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type
Nichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any Nichols algebras of diagonal type and plays a...
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| Format: | Article |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/8129361 |
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| author | Chen Qian Jing Wang |
| author_facet | Chen Qian Jing Wang |
| author_sort | Chen Qian |
| collection | DOAJ |
| description | Nichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any Nichols algebras of diagonal type and plays an important role in the classification of Nichols algebras of diagonal type with a finite root system. In this paper, the main properties of all simply connected Cartan graphs attached to rank 6 Nichols algebras of diagonal type are determined. As an application, we obtain a subclass of rank 6 finite dimensional Nichols algebras of diagonal type. |
| format | Article |
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| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-fdc9bf654237455f929e447274722fcd2025-02-03T05:43:48ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/81293618129361Finite Cartan Graphs Attached to Nichols Algebras of Diagonal TypeChen Qian0Jing Wang1Department of Mathematics, School of Science, Beijing Forestry University, 100083 Beijing, ChinaDepartment of Mathematics, School of Science, Beijing Forestry University, 100083 Beijing, ChinaNichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any Nichols algebras of diagonal type and plays an important role in the classification of Nichols algebras of diagonal type with a finite root system. In this paper, the main properties of all simply connected Cartan graphs attached to rank 6 Nichols algebras of diagonal type are determined. As an application, we obtain a subclass of rank 6 finite dimensional Nichols algebras of diagonal type.http://dx.doi.org/10.1155/2021/8129361 |
| spellingShingle | Chen Qian Jing Wang Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type Advances in Mathematical Physics |
| title | Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type |
| title_full | Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type |
| title_fullStr | Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type |
| title_full_unstemmed | Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type |
| title_short | Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type |
| title_sort | finite cartan graphs attached to nichols algebras of diagonal type |
| url | http://dx.doi.org/10.1155/2021/8129361 |
| work_keys_str_mv | AT chenqian finitecartangraphsattachedtonicholsalgebrasofdiagonaltype AT jingwang finitecartangraphsattachedtonicholsalgebrasofdiagonaltype |