✦ LIBER ✦
An endomorphism algebra realization problem and Kronecker embeddings for algebras of infinite representation type
✍ Scribed by Daniel Simson
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 120 KB
- Volume
- 172
- Category
- Article
- ISSN
- 0022-4049
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✦ Synopsis
Let R be a ÿnite-dimensional algebra over an algebraically closed ÿeld K. One of the main aims of this paper is to prove that if the algebra R is loop-ÿnite or R is strongly simply connected then the following three conditions are equivalent: (a) the algebra R is of inÿnite representation type, (b) the category mod(R) of ÿnitely generated right R-modules contains a full and exact subcategory equivalent with the category of Kronecker modules, (c) every K-algebra A is isomorphic to a K-algebra of the form EndR(X ), where X is a right R-module.