Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra
In this paper, we analyze the Lie bialgebra (LB) and quantize the generalized loop planar-Galilean conformal algebra (GLPGCA) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mo>...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/1/7 |
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| Summary: | In this paper, we analyze the Lie bialgebra (LB) and quantize the generalized loop planar-Galilean conformal algebra (GLPGCA) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></semantics></math></inline-formula>. Additionally, we prove that all LB structures on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></semantics></math></inline-formula> possess a triangular coboundary. We also quantize <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mo>(</mo><mo>Γ</mo><mo>)</mo></mrow></semantics></math></inline-formula> using the Drinfeld-twist quantization technique and identify a group of noncommutative algebras and noncocommutative Hopf algebras. |
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| ISSN: | 2075-1680 |