scholarly journals A duality map for quantum cluster varieties from surfaces

2017 ◽  
Vol 306 ◽  
pp. 1164-1208 ◽  
Author(s):  
Dylan G.L. Allegretti ◽  
Hyun Kyu Kim
Keyword(s):  
Quantum Cluster ◽  
Duality Map ◽  
Cluster Varieties

scholarly journals Laurent Positivity of Quantized Canonical Bases for Quantum Cluster Varieties from Surfaces

2019 ◽  
Vol 373 (2) ◽  
pp. 655-705 ◽  
Author(s):  
So Young Cho ◽  
Hyuna Kim ◽  
Hyun Kyu Kim ◽  
Doeun Oh
Keyword(s):  
Canonical Bases ◽  
Quantum Cluster ◽  
Cluster Varieties

scholarly journals Laurent phenomenon and simple modules of quiver Hecke algebras

2019 ◽  
Vol 155 (12) ◽  
pp. 2263-2295 ◽  
Author(s):  
Masaki Kashiwara ◽  
Myungho Kim
Keyword(s):  
Simple Module ◽  
Hecke Algebras ◽  
Duke Math ◽  
Cluster Algebras ◽  
Coordinate Ring ◽  
Simple Modules ◽  
Laurent Phenomenon ◽  
Cluster Variable ◽  
Quantum Cluster

In this paper we study consequences of the results of Kang et al. [Monoidal categorification of cluster algebras, J. Amer. Math. Soc. 31 (2018), 349–426] on a monoidal categorification of the unipotent quantum coordinate ring $A_{q}(\mathfrak{n}(w))$ together with the Laurent phenomenon of cluster algebras. We show that if a simple module $S$ in the category ${\mathcal{C}}_{w}$ strongly commutes with all the cluster variables in a cluster $[\mathscr{C}]$, then $[S]$ is a cluster monomial in $[\mathscr{C}]$. If $S$ strongly commutes with cluster variables except for exactly one cluster variable $[M_{k}]$, then $[S]$ is either a cluster monomial in $[\mathscr{C}]$ or a cluster monomial in $\unicode[STIX]{x1D707}_{k}([\mathscr{C}])$. We give a new proof of the fact that the upper global basis is a common triangular basis (in the sense of Qin [Triangular bases in quantum cluster algebras and monoidal categorification conjectures, Duke Math. 166 (2017), 2337–2442]) of the localization $\widetilde{A}_{q}(\mathfrak{n}(w))$ of $A_{q}(\mathfrak{n}(w))$ at the frozen variables. A characterization on the commutativity of a simple module $S$ with cluster variables in a cluster $[\mathscr{C}]$ is given in terms of the denominator vector of $[S]$ with respect to the cluster $[\mathscr{C}]$.

Being versus becoming ontology of paradox management

2016 ◽  
Vol 23 (4) ◽  
pp. 558-562 ◽  
Author(s):  
Runtian Jing ◽  
Andrew H. Van de Ven
Keyword(s):  
Theoretical Explanation ◽  
Management Research ◽  
Basic Premise ◽  
Content Type ◽  
Theoretical Contribution ◽  
Eastern Culture ◽  
Yin Yang ◽  
Extreme Groups ◽  
Duality Map ◽  
Being And Becoming

Purpose The purpose of this paper is to discuss the theoretical contribution of Li’s (2016) “Yin-Yang balancing” approach of paradox management, as well as its future development to guide paradox management research across the east and west contexts. Design/methodology/approach It begins by recognizing the importance of paradox management research, especially the indigenous epistemological approach as Li (2016) has followed. The authors take “being” and “becoming” ontology toward social reality as the basic premise in this commentary, and summarize the knowledge that the study has contributed to existing literature. Findings The “Yin-Yang balancing” approach can extend the knowledge about paradox management phenomena at least from four aspects: the “either/and” frame to view a paradox system, the importance of “seed” or “threshold” in defining moderate rather than extreme groups, duality map as a novel tool for paradox management, and comparison of being and becoming ontology. Originality/value Based on the comparison of “being” and “becoming” ontological view, the authors suggest to further develop this “Yin-Yang balancing” approach by emphasizing the following issues: eastern culture does not have exclusive ownership of the “becoming” ontology toward the world, elaboration of alternative theoretical explanation to win out the identity approach about organizational existence, the linkage between the “Yin-Yang balancing” epistemological system and process research method, and boundary condition of the “Yin-Yang balancing” approach.

Ag7Au6: A 13-Atom Alloy Quantum Cluster

2012 ◽  
Vol 51 (9) ◽  
pp. 2155-2159 ◽  
Author(s):  
Thumu Udayabhaskararao ◽  
Yan Sun ◽  
Nirmal Goswami ◽  
Samir K. Pal ◽  
K. Balasubramanian ◽  
...  
Keyword(s):  
Quantum Cluster

scholarly journals Comparison of two-quantum-cluster approximations

2002 ◽  
Vol 65 (4) ◽  
Author(s):  
Th. A. Maier ◽  
M. Jarrell
Keyword(s):  
Quantum Cluster
Sign in / Sign up

Export Citation Format

Share Document