Noncommutative Birational Geometry, Representations and Combinatorics
About this Title
Arkady Berenstein, University of Oregon, Eugene, OR and Vladimir Retakh, Rutgers University, Piscataway, NJ, Editors
Publication: Contemporary Mathematics
Publication Year 2013: Volume 592
ISBNs: 978-0-8218-8980-0 (print); 978-1-4704-0971-5 (online)
This volume contains the proceedings of the AMS Special Session on Noncommutative Birational Geometry, Representations and Cluster Algebras, held from January 6–7, 2012, in Boston, MA.
The papers deal with various aspects of noncommutative birational geometry and related topics, focusing mainly on structure and representations of quantum groups and algebras, braided algebras, rational series in free groups, Poisson brackets on free algebras, and related problems in combinatorics.
This volume is useful for researchers and graduate students in mathematics and mathematical physics who want to be introduced to different areas of current research in the new area of noncommutative algebra and geometry.
Graduate students and research mathematicians interested in noncommutative geometry and related topics, including representations and cluster algebras.
Table of Contents
- Roland Bacher and Christophe Reutenauer – The number of right ideals of given codimension over a finite field
- Yuri Bazlov and Arkady Berenstein – Cocycle twists and extensions of braided doubles
- Arkady Berenstein and Jacob Greenstein – Quantum Chevalley groups
- Arkady Berenstein, Vladimir Retakh, Christophe Reutenauer and Doron Zeilberger – The Reciprocal of for non-commuting and , Catalan numbers and non-commutative quadratic equations
- Andrew T. Carroll and Jerzy Weyman – Semi-invariants for gentle algebras
- Sachin Gautam and Valerio Toledano Laredo – Monodromy of the trigonometric Casimir connection for
- Aaron Lauve and Christophe Reutenauer – Rational series in the free group and the Connes operator
- Kyungyong Lee and Li Li – On natural maps from strata of quiver Grassmannians to ordinary Grassmannians
- David Nacin – Properties of a Minimal Non-Koszul
- Alexander Odesskii, Vladimir Rubtsov and Vladimir Sokolov – Double Poisson brackets on free associative algebras
- Michaela Vancliff and Padmini P. Veerapen – Generalizing the notion of rank to noncommutative quadratic forms