Short Course

Roozbeh Hazrat Western Sydney University
The curious case of Leavitt algebras

In 1960's Bill Leavitt considered free unital algebras over 2n symbols {xi, ... ,xn} and {yi, ... ,yn} modulo two specific relations, roughly, sum_(i=1)^n x_iy_i  and xiyj = oij. He proved these rings have no IBN and are simple rings. The algebras now called Leavittpath algebras where introduced over a decade ago, by considering a direct graph with vertices and edges and placing the Leavitt's relation on each node. Since then there have been, astonishingly, over 150 papers on these algebras, mainly devoted to find out the ring properties of these algebras for specific type of graphs and the classification of these algebras via suitable invariants. We introduce these algebras and give a summary of results known about them. We then describe its generalization to weighted Leavitt algebras. The talks are accessible to interested undergraduate students.

Date & Time: 
June 30, 2018, 10:00 to 11:00
June 30, 2018, 11:30 to 12:30
Room 217, Dept. Math. Sci., Sharif University of Technology