Representation dimension of generalized path algebras of cyclic quivers. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Eshraghi, Hossein
• Is Part Of: Communications in algebra. Volume 45:Issue 6(2017)
• Page Start: 2296
• Page End: 2305
• Publication Date: 2017-06-03
• Subjects: Quiver representations -- representation dimension -- representation type of an algebra; 16G20 -- 16G60 -- 16G10 -- 16G99; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233197
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let Λ be a non semisimple symmetric artin algebra over a commutative artinian ring R and let repdim ( Λ ) be its representation dimension. Assume also that 𝒬 is a finite quiver whose connected components are amalgamations of single cycles possibly with multiple arrows, and that ℐ is an admissible ideal in the generalized path algebra Λ 𝒬 . We prove that r e p d i m ( Λ 𝒬 ℐ ) ≤ repdim ( Λ )+1.