Professor Anne Shepler invites you to attend the Master's Project Defense of Isaac Bancroft.

WHEN: Thursday, September 23rd at 12:00pm in GAB 461

"Resolutions of Ore Extensions"

ABSTRACT:
Non-commutative algebras arise in various settings in mathematics. In 1995, Cap, Schichl, and Vanzura formally represented many such algebras in non-commutative differential geometry as twisted tensor products. To each we may assign a "twisting map" to record the non-commutative structure and organize homological information. Ore extensions are a type of twisted tensor product which include Weyl algebras, quantum polynomial rings, and universal enveloping algebras as special cases. By recognizing Ore extensions as twisted tensor products, we may construct a resolution for a large class of Ore extensions and demonstrate that it recovers the Chevalley-Eilenberg resolution for universal enveloping algebras.