The quantum dilogarithm and representations of quantum cluster varieties

The quantum dilogarithm and representations of quantized cluster varieties

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...

The quantum dilogarithm and unitary representations of cluster modular groupoids

2 The symplectic double of a cluster X -variety 9 2.1 Cluster X and A-varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Construction of the symplectic double . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 A decomposition of mutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 The motivic dilogarithm structure on the sym...

On cluster theory and quantum dilogarithm identities

These are expanded notes from three survey lectures given at the 14th International Conference on Representations of Algebras (ICRA XIV) held in Tokyo in August 2010. We first study identities between products of quantum dilogarithm series associated with Dynkin quivers following Reineke. We then examine similar identities for quivers with potential and link them to Fomin-Zelevinsky’s theory of...

A Cluster-Based Hybrid broadcasting mechanism for Quantum Systems with Power Management and delay Constraint in the MAC sub-layer

اثر تنش اسمزی بر برخی خصوصیات فیزیولوژیکی ارقام گندم

This study was conducted to evaluate the effect of osmotic stress on physiological characters of wheat cultivars as a factorial experiment based on completely randomized design with three replications in 2012 at the Mohaghegh Ardabili University. Twenty wheat cultivars studied in three stress levels (control, -6 and -12 Bars). Analysis of variance showed that the stress had significant effect o...