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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/128 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |