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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2024-12-01
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| author | Yu Yang Xingtao Wang |
| author_facet | Yu Yang Xingtao Wang |
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| description | 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. |
| format | Article |
| id | doaj-art-e336ca7523294978966bd60ff098114e |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-e336ca7523294978966bd60ff098114e2025-01-24T13:22:07ZengMDPI AGAxioms2075-16802024-12-01141710.3390/axioms14010007Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal AlgebraYu Yang0Xingtao Wang1School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaIn 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.https://www.mdpi.com/2075-1680/14/1/7generalized loop planar-Galilean conformal algebraLie bialgebraquantization |
| spellingShingle | Yu Yang Xingtao Wang Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra Axioms generalized loop planar-Galilean conformal algebra Lie bialgebra quantization |
| title | Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra |
| title_full | Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra |
| title_fullStr | Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra |
| title_full_unstemmed | Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra |
| title_short | Lie Bialgebra Structures and Quantization of Generalized Loop Planar Galilean Conformal Algebra |
| title_sort | lie bialgebra structures and quantization of generalized loop planar galilean conformal algebra |
| topic | generalized loop planar-Galilean conformal algebra Lie bialgebra quantization |
| url | https://www.mdpi.com/2075-1680/14/1/7 |
| work_keys_str_mv | AT yuyang liebialgebrastructuresandquantizationofgeneralizedloopplanargalileanconformalalgebra AT xingtaowang liebialgebrastructuresandquantizationofgeneralizedloopplanargalileanconformalalgebra |