Abstract
A method is described for constructing the minimal projective resolution of an algebra considered as a bimodule over itself. The method applies to an algebra presented as the quotient of a tensor algebra over a separable algebra by an ideal of relations that is either homogeneous or admissible (with some additional finiteness restrictions in the latter case). In particular, it applies to any finite-dimensional algebra over an algebraically closed field. The method is illustrated by a number of examples, viz. truncated algebras, monomial algebras, and Koszul algebras, with the aim of unifying existing treatments of these in the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 323-362 |
| Number of pages | 40 |
| Journal | Journal of Algebra |
| Volume | 212 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 1999 |
Funding
Most of the work on this paper, including several early versions, was carried out at the University of Liverpool, where the second author was supported by a grant from the Engineering and Physical Sciences Research Council. We also thank the SFB 343 at the University of Bielefeld for its hospitality during the preparation of the final version. We are particularly grateful to Lutz Hille for enlightening discussions about Koszul algebras, which enabled us to write Section 9, and to Wolfgang Soergel and Mike Bardzell for sending us their preprints, wBGSx and wBax, respectively.
| Funders | Funder number |
|---|---|
| Engineering and Physical Sciences Research Council |
ASJC Scopus subject areas
- Algebra and Number Theory