Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub>
The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub><...
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1293 |
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| author | Shilin Yang Yongfeng Zhang |
| author_facet | Shilin Yang Yongfeng Zhang |
| author_sort | Shilin Yang |
| collection | DOAJ |
| description | The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub><mrow><mo>[</mo><mi>z</mi><mo>;</mo><mi>σ</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula> of automorphism type for the Sweedler<inline-formula><math display="inline"><semantics><msup><mrow></mrow><mo>′</mo></msup></semantics></math></inline-formula>s 4-dimensional Hopf algebra <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub></semantics></math></inline-formula>. Firstly, we calculate all equivalent classes of twisted homomorphisms <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>σ</mi><mo>,</mo><mi>J</mi><mo>)</mo></mrow></semantics></math></inline-formula> for <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub></semantics></math></inline-formula>. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub><mrow><mo>[</mo><mi>z</mi><mo>;</mo><mi>σ</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula> up to isomorphism. |
| first_indexed | 2024-03-10T17:57:55Z |
| format | Article |
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| language | English |
| last_indexed | 2024-03-10T17:57:55Z |
| publishDate | 2020-08-01 |
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| series | Mathematics |
| spelling | doaj.art-53d3c961194b487eb25b03ea903052802023-11-20T09:08:02ZengMDPI AGMathematics2227-73902020-08-0188129310.3390/math8081293Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub>Shilin Yang0Yongfeng Zhang1School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, ChinaSchool of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, ChinaThe aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub><mrow><mo>[</mo><mi>z</mi><mo>;</mo><mi>σ</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula> of automorphism type for the Sweedler<inline-formula><math display="inline"><semantics><msup><mrow></mrow><mo>′</mo></msup></semantics></math></inline-formula>s 4-dimensional Hopf algebra <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub></semantics></math></inline-formula>. Firstly, we calculate all equivalent classes of twisted homomorphisms <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>σ</mi><mo>,</mo><mi>J</mi><mo>)</mo></mrow></semantics></math></inline-formula> for <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub></semantics></math></inline-formula>. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">H</mi><mn>4</mn></msub><mrow><mo>[</mo><mi>z</mi><mo>;</mo><mi>σ</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula> up to isomorphism.https://www.mdpi.com/2227-7390/8/8/1293Ore extensionDrinfeld twisttwisted homomorphismHopf algebra |
| spellingShingle | Shilin Yang Yongfeng Zhang Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub> Mathematics Ore extension Drinfeld twist twisted homomorphism Hopf algebra |
| title | Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub> |
| title_full | Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub> |
| title_fullStr | Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub> |
| title_full_unstemmed | Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub> |
| title_short | Ore Extensions for the Sweedler’s Hopf Algebra <i>H</i><sub>4</sub> |
| title_sort | ore extensions for the sweedler s hopf algebra i h i sub 4 sub |
| topic | Ore extension Drinfeld twist twisted homomorphism Hopf algebra |
| url | https://www.mdpi.com/2227-7390/8/8/1293 |
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