Invertible bimodule categories over the representation category of a Hopf algebra

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• 作者：Bojana Femi膰^a ; Adriana Mejí ; a Castañ ; o^b ; Martí ; n Mombelli^b ;
• 关键词：18D10 ; 16W30 ; 19D23
• 刊名：Journal of Pure and Applied Algebra
• 出版年：November 2014
• 年：2014
• 卷：218
• 期：11
• 页码：2096-2118
• 全文大小：418 K

文摘

For any finite-dimensional Hopf algebra H   we construct a group homomorphism 22404914000577&_mathId=si1.gif&_user=111111111&_pii=S0022404914000577&_rdoc=1&_issn=00224049&md5=8b18227de60798fe7c5c040a935cc357" title="Click to view the MathML source">BiGal(H)→BrPic(Rep(H))$\mathrm{BiGal}(H)\to \text{BrPic}(\mathrm{Rep}(H))$, from the group of equivalence classes of H  -biGalois objects to the group of equivalence classes of invertible exact 22404914000577&_mathId=si2.gif&_user=111111111&_pii=S0022404914000577&_rdoc=1&_issn=00224049&md5=227b87d838e76ac0a14d19ff013d16b0" title="Click to view the MathML source">Rep(H)$\mathrm{Rep}(H)$-bimodule categories. We discuss the injectivity of this map. We exemplify in the case 22404914000577&_mathId=si3.gif&_user=111111111&_pii=S0022404914000577&_rdoc=1&_issn=00224049&md5=c85cf3fcedd462605356b112d76677da" title="Click to view the MathML source">H=T_q$H=T_q$ is a Taft Hopf algebra and for this we classify all exact indecomposable 22404914000577&_mathId=si4.gif&_user=111111111&_pii=S0022404914000577&_rdoc=1&_issn=00224049&md5=337b29751eafcb0257200a0c5c5bdf18" title="Click to view the MathML source">Rep(T_q)$\mathrm{Rep}(T_q)$-bimodule categories.