Multiparameter Quantum Supergroups, Deformations and Specializations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917553809391616 |
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| author | García, Gastón Andrés Gavarini, Fabio Paolini, Margherita |
| author_facet | García, Gastón Andrés Gavarini, Fabio Paolini, Margherita |
| contents | In this paper we introduce a multiparameter version of the quantum universal enveloping superalgebras introduced by Yamane in [H. Yamane, "Quantized enveloping algebras associated to simple Lie superalgebras and their universal $R$-matrices", Publ. Res. Inst. Math. Sci. 30 (1994), no. 1, 15-87]. For these objects we consider:
- (1) their deformations by twist and by 2-cocycle (both of "toral type"); in particular, we prove that this family is stable under both types of deformations;
- (2) their semiclassical limits, which are multiparameter Lie superbialgebras;
- (3) the deformations by twist and by 2-cocycle (of "toral type") of these multiparameter Lie superbialgebras: in particular, we prove that this family is stable under these deformations, and that "quantization commutes with deformation". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiparameter Quantum Supergroups, Deformations and Specializations García, Gastón Andrés Gavarini, Fabio Paolini, Margherita Quantum Algebra Mathematical Physics Rings and Algebras 17B37, 17B62 In this paper we introduce a multiparameter version of the quantum universal enveloping superalgebras introduced by Yamane in [H. Yamane, "Quantized enveloping algebras associated to simple Lie superalgebras and their universal $R$-matrices", Publ. Res. Inst. Math. Sci. 30 (1994), no. 1, 15-87]. For these objects we consider: - (1) their deformations by twist and by 2-cocycle (both of "toral type"); in particular, we prove that this family is stable under both types of deformations; - (2) their semiclassical limits, which are multiparameter Lie superbialgebras; - (3) the deformations by twist and by 2-cocycle (of "toral type") of these multiparameter Lie superbialgebras: in particular, we prove that this family is stable under these deformations, and that "quantization commutes with deformation". |
| title | Multiparameter Quantum Supergroups, Deformations and Specializations |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras 17B37, 17B62 |
| url | https://arxiv.org/abs/2410.22549 |