Hopf Differential Graded Galois Extensions
We introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra <i>H</i> and an <i>H</i>-module dg algebra <i>R</i>, we show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display=&q...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/1/128 |
| _version_ | 1797406791337771008 |
|---|---|
| author | Bo-Ye Zhang |
| author_facet | Bo-Ye Zhang |
| author_sort | Bo-Ye Zhang |
| collection | DOAJ |
| description | We introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra <i>H</i> and an <i>H</i>-module dg algebra <i>R</i>, we show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">D</mi><mrow><mo>(</mo><mi>R</mi><mo>#</mo><mi>H</mi><mo>)</mo></mrow><mo>≅</mo><mi mathvariant="script">D</mi><mrow><mo>(</mo><msup><mi>R</mi><mi>H</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is equivalent to that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>/</mo><msup><mi>R</mi><mi>H</mi></msup></mrow></semantics></math></inline-formula> is a Hopf differential graded Galois extension. We present a weaker version of Hopf differential graded Galois extensions and show the relationships between Hopf differential graded Galois extensions and Hopf Galois extensions. |
| first_indexed | 2024-03-09T03:31:44Z |
| format | Article |
| id | doaj.art-aef2cd264c1d4fb0bf9c78d927b640b3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T03:31:44Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aef2cd264c1d4fb0bf9c78d927b640b32023-12-03T14:54:47ZengMDPI AGMathematics2227-73902022-12-0111112810.3390/math11010128Hopf Differential Graded Galois ExtensionsBo-Ye Zhang0School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, ChinaWe introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra <i>H</i> and an <i>H</i>-module dg algebra <i>R</i>, we show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">D</mi><mrow><mo>(</mo><mi>R</mi><mo>#</mo><mi>H</mi><mo>)</mo></mrow><mo>≅</mo><mi mathvariant="script">D</mi><mrow><mo>(</mo><msup><mi>R</mi><mi>H</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is equivalent to that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>/</mo><msup><mi>R</mi><mi>H</mi></msup></mrow></semantics></math></inline-formula> is a Hopf differential graded Galois extension. We present a weaker version of Hopf differential graded Galois extensions and show the relationships between Hopf differential graded Galois extensions and Hopf Galois extensions.https://www.mdpi.com/2227-7390/11/1/128differential graded algebrasderived categoriesGalois extensions |
| spellingShingle | Bo-Ye Zhang Hopf Differential Graded Galois Extensions Mathematics differential graded algebras derived categories Galois extensions |
| title | Hopf Differential Graded Galois Extensions |
| title_full | Hopf Differential Graded Galois Extensions |
| title_fullStr | Hopf Differential Graded Galois Extensions |
| title_full_unstemmed | Hopf Differential Graded Galois Extensions |
| title_short | Hopf Differential Graded Galois Extensions |
| title_sort | hopf differential graded galois extensions |
| topic | differential graded algebras derived categories Galois extensions |
| url | https://www.mdpi.com/2227-7390/11/1/128 |
| work_keys_str_mv | AT boyezhang hopfdifferentialgradedgaloisextensions |