Noncommutative Birational Geometry, Representations and Combinatorics

ISBN-13: 9780821889800 / Angielski

Opis

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.

Spis treści

Table of Contents:<ul><li>The number of right ideals of given codimension over a finite field by R. Bacher and C. Reutenauer </li><li>Cocycle twists and extensions of braided doubles by Y. Bazlov and A. Berenstein </li><li>Quantum Chevalley groups by A. Berenstein and J. Greenstein </li><li>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</li><li> Semi-invariants for gentle algebras by A. Carroll and J. Weyman </li><li>Monodromy of the trigonometric Casimir connection for $\mathfrak_2$ by S. Gautam and V. T. Laredo </li><li>Rational series in the free group and the Connes operator by A. Lauve and C. Reutenauer </li><li>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 </li><li>Double Poisson brackets on free associative algebras by A. Odesskii, V. Rubtsov, and V. Sokolov </li><li>Generalizing the notion of rank to noncommutative quadratic forms by M. Vancliff and P. P. Veerapen </li></ul>