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.
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978-0-8218-8980-0 (9780821889800)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Arkady Berenstein, University of Oregon, Eugene, OR, USA.
Vladimir Retakh, Rutgers University, Piscataway, NJ, USA.
Table of Contents:
The number of right ideals of given codimension over a finite field by R. Bacher and C. Reutenauer
Cocycle twists and extensions of braided doubles by Y. Bazlov and A. Berenstein
Quantum Chevalley groups by A. Berenstein and J. Greenstein
The reciprocal of $\Sigma_{n\geq 0}a^nb^n$ for non-commuting $a$ and $b_1$, Catalan numbers and non-commutative quadratic equations by A. Berenstein, V. Retakh, C. Reutenauer, and D. Zeilberger
Semi-invariants for gentle algebras by A. Carroll and J. Weyman
Monodromy of the trigonometric Casimir connection for $\mathfrak{sl}_2$ by S. Gautam and V. T. Laredo
Rational series in the free group and the Connes operator by A. Lauve and C. Reutenauer
On natural maps from strata of quiver Grassmannians to ordinary Grassmannians by K. Lee and L. Li Properties of a minimal non-Koszul $A(\Gamma)$ by D. Nacin
Double Poisson brackets on free associative algebras by A. Odesskii, V. Rubtsov, and V. Sokolov
Generalizing the notion of rank to noncommutative quadratic forms by M. Vancliff and P. P. Veerapen
