Flat matrix models for quantum permutation groups

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• 作者：Teodor Banica^a ; ^{teodor.banica@u-cergy.fr" class="auth_mail" title="E-mail the corresponding author} ; Ion Nechita^b ; ^{nechita@irsamc.ups-tlse.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16T05 ; 46L54
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：83
• 期：Complete
• 页码：24-46
• 全文大小：434 K

文摘

We study the matrix models class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S019688581630077X&_mathId=si1.gif&_user=111111111&_pii=S019688581630077X&_rdoc=1&_issn=01968858&md5=5aa119203f7f345baf651621ff7ff1cc">class="imgLazyJSB inlineImage" height="18" width="177" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S019688581630077X-si1.gif">class="mathContainer hidden">class="mathCode">$\pi :C(S_N^{+})\to M_N(C(X))$ which are flat, in the sense that the standard generators of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S019688581630077X&_mathId=si2.gif&_user=111111111&_pii=S019688581630077X&_rdoc=1&_issn=01968858&md5=81fad8db5b9dd456706b17879b3e8ee2">class="imgLazyJSB inlineImage" height="18" width="48" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S019688581630077X-si2.gif">class="mathContainer hidden">class="mathCode">$C(S_N^{+})$ are mapped to rank 1 projections. Our first result is a generalization of the Pauli matrix construction at class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S019688581630077X&_mathId=si3.gif&_user=111111111&_pii=S019688581630077X&_rdoc=1&_issn=01968858&md5=b92e1ece3675ec71522e997ab65126a5" title="Click to view the MathML source">N=4class="mathContainer hidden">class="mathCode">$N=4$, using finite groups and 2-cocycles. Our second result is the construction of a universal representation of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S019688581630077X&_mathId=si2.gif&_user=111111111&_pii=S019688581630077X&_rdoc=1&_issn=01968858&md5=81fad8db5b9dd456706b17879b3e8ee2">class="imgLazyJSB inlineImage" height="18" width="48" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S019688581630077X-si2.gif">class="mathContainer hidden">class="mathCode">$C(S_N^{+})$, inspired from the Sinkhorn algorithm, that we conjecture to be inner faithful.