发表机构
Dipartimento di Matematica Università di Roma Tor Vergata（罗马托尔维加塔大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广扭曲$C^*$-张量积中的对称态研究，证明仅厄米二元特征情形可行，并给出三种情形下的德菲内蒂定理真正版本，另发现克莱因四元群扭曲模型可详尽处理。
AI 中文摘要
作者在前两篇论文中详尽研究了扭曲$C^*$-张量积。在此新背景下，推广通常的张量积与费米子张量积，我们分析在无限扭曲$C^*$-张量积中研究对称态（即对所有有限置换不变的态）集合的可能性。作为初步结果，我们认识到仅当构造此类扭曲张量积所涉及的二元特征为厄米特征时，此类研究才能进行。否则，有限对称群在无限扭曲链上不存在自然作用。此外，尽管对基于厄米二元特征的所有扭曲系统而言，对称态的研究确实有意义，但研究表明仅在三种情形下才能富有成效地进行。在这些情形中，我们能够提供著名的德菲内蒂定理的“真正”版本，该定理已由休伊特和萨维奇针对一般经典情形、斯托默针对通常张量积、菲达莱奥针对费米子模型分别建立。非常令人惊讶的是，出现了一种可被详尽处理的额外扭曲模型：它对应于由所谓的克莱因四元群及其在等价意义下唯一的克莱因二元特征所扭曲的链。
英文摘要
The twisted $C^*$-tensor product was exhaustively investigated by the authors in two previous papers. In this new context, generalising the usual tensor product and the Fermi one, we analyse the possibility of studying the set of symmetric states, that is those invariant under all finite permutations, in the setting of infinite twisted $C^*$-tensor products. As a preliminary result, we recognise that such an investigation can proceed only when the bicharacter, involved in the construction of such twisted tensor products, is hermitian. Otherwise, there is no natural action of the finitary symmetric group on the infinite twisted chain. Furthermore, even if the investigation of symmetric states is certainly meaningful for all twisted systems based on hermitian bicharacters, it is shown that it can be fruitfully carried out in three cases only. In these cases, we can provide the "genuine" version of the celebrated De Finetti Theorem already established by Hewitt and Savage for the general classical case, Stormer for the usual tensor product and Fidaleo for Fermi models. Very surprisingly, it emerges that one more twisted model can be treated exhaustively: it corresponds to the chain twisted by the so-called Klein four-group, and its Klein bicharacter unique up to equivalence.
CommentsTo appear in "Annales Henri Poincaré"
