Some homological aspects of idempotents in idempotented algebras

Abstract

We study special idempotents (as described by Bushnell and Kutzko) and split idempotents in the context of module and derived categories for idempotented algebras. We then characterize these concepts for path algebras of quivers.

Keywords:

• Idempotented algebras
• path algebras
• special idempotents

2010 Mathematics Subject Classification:

• Primary: 16E99
• Secondary: 16Y99
• 16E35
• 22E50
• 16D90

Acknowledgements

Both authors would like to thank the Tata Institute of Fundamental Research, Mumbai, for providing an effective environment in which a part of this work was done, Sandeep Varma for his suggestions, and the anonymous referee for their suggestions and comments.