Pentagon Relation for the Quantum Dilogarithm and Quantized M
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منابع مشابه
A proof of the pentagon relation for the quantum dilogarithm
1 Introduction The quantum dilogarithm function is given by the following integral: Φ h (z) := exp − 1 4 Ω e −ipz sh(πp)sh(πhp) dp p , sh(p) = e p − e −p 2. Here Ω is a path from −∞ to +∞ making a little half circle going over the zero. So the integral is convergent. It goes back to Barnes [Ba], and appeared in many papers during the last 30 years: • The function Φ h (z) is meromorphic with pol...
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We study the knot invariant based on the quantum dilogarithm function. This invariant can be regarded as a non-compact analogue of Kashaev’s invariant, or the colored Jones invariant, and is defined by an integral form. The 3-dimensional picture of our invariant originates from the pentagon identity of the quantum dilogarithm function, and we show that the hyperbolicity consistency conditions i...
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To David Kazhdan for his 60th birthday " Loxadь sostoit iz trh neravnyh polovin ". 4 The quantum dilogarithm and its properties 26 4.1 The quantum logarithm function and its properties. . 1 " A horse consists of three unequal halves ". cf. A. de Barr, Horse doctor. Moscow 1868. Cluster varieties [FG2] are relatives of cluster algebras [FZI]. Cluster modular groups act by automor-phisms of clust...
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تاریخ انتشار 2008