B-Construction and C-Construction

Abstract

B-construction is a way of obtaining a graded algebra from the triple consisting of an additive category, an object, and an autoequivalence, while C-construction is a way of obtaining an algebra (without unity) from the pair consisting of an additive category and a set of objects. In this article, we study and compare three important classes of algebras in noncommutative algebraic geometry and representation theory of finite dimensional algebras, namely, quantum polynomial algebras, preprojetive algebras and trivial extensions, via these constructions.

Key Words:

• Preprojective algebras
• Quantum polynomial algebras
• Trivial extensions

2010 Mathematics Subject Classification:

• 16S38
• 16S50
• 16S37
• 16W50

ACKNOWLEDGMENT

We thank Minamoto for many useful discussions concerning this article.

This work was supported by Grant-in-Aid for Scientific Research (C) 91540020.

Notes

Communicated by D. Zacharia.