Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras PDF Download
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Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 1470436949
Category : Mathematics
Languages : en
Pages : 134
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Book Description
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 1470436949
Category : Mathematics
Languages : en
Pages : 134
Get Book Here
Book Description
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts
Author: K. R Goodearl
Publisher: American Mathematical Society
ISBN: 1470467356
Category : Mathematics
Languages : en
Pages : 112
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Book Description
View the abstract.
Author: Mee Seong Im
Publisher: American Mathematical Society
ISBN: 1470470349
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.
Author: Sergio R. López-Permouth
Publisher: American Mathematical Soc.
ISBN: 1470435551
Category : Mathematics
Languages : en
Pages : 298
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Book Description
This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.
Author: Xiao Xiong
Publisher: American Mathematical Soc.
ISBN: 1470428067
Category : Mathematics
Languages : en
Pages : 130
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Book Description
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.
Author: James Damon
Publisher: American Mathematical Soc.
ISBN: 1470426803
Category : Mathematics
Languages : en
Pages : 180
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Book Description
The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions in which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries in a generic way. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the “positional geometry” of the collection. The linking structure extends in a minimal way the individual “skeletal structures” on each of the regions. This allows the authors to significantly extend the mathematical methods introduced for single regions to the configuration of regions.
Author: Vladimir K. Dobrev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110609711
Category : Mathematics
Languages : en
Pages : 337
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Book Description
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This fourth volume covers AdS/CFT, Virasoro and affine (super-)algebras.
Author: Marius Junge
Publisher: American Mathematical Soc.
ISBN: 1470425653
Category : Mathematics
Languages : en
Pages : 102
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Book Description
In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive inequalities with respect to the Markov process given by the word length and with an even integer. Interpolation and differentiation also yield general hypercontrativity for via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part—which varies from one group to another—is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T).
Author: John McCuan
Publisher: American Mathematical Soc.
ISBN: 1470409380
Category : Mathematics
Languages : en
Pages : 122
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Book Description
The author considers the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. He also considers as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.
Author: Stefano Bianchini
Publisher: American Mathematical Soc.
ISBN: 1470427664
Category : Mathematics
Languages : en
Pages : 124
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Book Description
The authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.
