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NCTS Mini-Course on Representations of Algebras and Tilting Modules
 
4/13 (Fri.), 4/16 (Mon.), 4/18 (Wed.) 9:30 - 11:30, April 13 - 18, 2018
,

Speaker:
Changchang Xi (Capital Normal University)


Organizers:
Yong-jie Wang (NCTS)
Chia-Fu Yu (Academia Sinica)


Venue:
4/13, 4/18: Rm 201, NCTS (Astro-Math Bldg., NTU)
4/16: Rm 202, NCTS (Astro-Math Bldg., NTU)
 
Title:
Representations of Algebras and Tilting Modules
 
Abstract:
In this series of three lectures, we shall introduce basic knowledge on representations of finite-dimensional algebras. First, we give a description of algebras and representations by quivers with relations, and then describe representation-finite algebras by Dynkin diagrams. This is the famous Gabriel classification theorem and closely related to root systems of simple Lie algebras. Finally, we discuss a special class of representations of algebras, called tilting modules, and mention some of their homological properties. Tilting modules provide a class of derived equivalences and appear often in categories of highest weight categories of representations of Lie algebras, while the bridge between tilting modules and highest weight categories is the finite-dimensional quasi-hereditary algebras introduced by Cline-Parshall-Scott.





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