Twisted tensor products of quantum affine vertex algebras and coproducts
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929303350935552 |
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| author | Kong, Fei |
| author_facet | Kong, Fei |
| contents | Let $\mathfrak g$ be a symmetrizable Kac-Moody Lie algebra, and let $V_{\hat{\mathfrak g},\hbar}^\ell$, $L_{\hat{\mathfrak g},\hbar}^\ell$ be the quantum affine vertex algebras constructed in [11]. For any complex numbers $\ell$ and $\ell'$, we present an $\hbar$-adic quantum vertex algebra homomorphism $Δ$ from $V_{\hat{\mathfrak g},\hbar}^{\ell+\ell'}$ to the twisted tensor product $\hbar$-adic quantum vertex algebra $V_{\hat{\mathfrak g},\hbar}^\ell\widehat\otimes V_{\hat{\mathfrak g},\hbar}^{\ell'}$. In addition, if both $\ell$ and $\ell'$ are positive integers, we show that $Δ$ induces an $\hbar$-adic quantum vertex algebra homomorphism from $L_{\hat{\mathfrak g},\hbar}^{\ell+\ell'}$ to the twisted tensor product $\hbar$-adic quantum vertex algebra $L_{\hat{\mathfrak g},\hbar}^\ell\widehat\otimes L_{\hat{\mathfrak g},\hbar}^{\ell'}$. Moreover, we prove the coassociativity of $Δ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted tensor products of quantum affine vertex algebras and coproducts Kong, Fei Quantum Algebra 17B69 Let $\mathfrak g$ be a symmetrizable Kac-Moody Lie algebra, and let $V_{\hat{\mathfrak g},\hbar}^\ell$, $L_{\hat{\mathfrak g},\hbar}^\ell$ be the quantum affine vertex algebras constructed in [11]. For any complex numbers $\ell$ and $\ell'$, we present an $\hbar$-adic quantum vertex algebra homomorphism $Δ$ from $V_{\hat{\mathfrak g},\hbar}^{\ell+\ell'}$ to the twisted tensor product $\hbar$-adic quantum vertex algebra $V_{\hat{\mathfrak g},\hbar}^\ell\widehat\otimes V_{\hat{\mathfrak g},\hbar}^{\ell'}$. In addition, if both $\ell$ and $\ell'$ are positive integers, we show that $Δ$ induces an $\hbar$-adic quantum vertex algebra homomorphism from $L_{\hat{\mathfrak g},\hbar}^{\ell+\ell'}$ to the twisted tensor product $\hbar$-adic quantum vertex algebra $L_{\hat{\mathfrak g},\hbar}^\ell\widehat\otimes L_{\hat{\mathfrak g},\hbar}^{\ell'}$. Moreover, we prove the coassociativity of $Δ$. |
| title | Twisted tensor products of quantum affine vertex algebras and coproducts |
| topic | Quantum Algebra 17B69 |
| url | https://arxiv.org/abs/2404.03550 |