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Resolutions over Koszul algebras | | E. L. Green
; G. Hartman
; E. N. Marcos
; O. Solberg
; | | Date: |
9 Sep 2004 | | Journal: | Arch. Math., 85 (2005), no. 2, 118-127 DOI: 10.1007/s00013-005-1299-9 | | Subject: | Rings and Algebras; Representation Theory MSC-class: 16S37, 16E05, 16W50 | math.RA math.RT | | Abstract: | In this paper we show that if $Lambda=amalg_{igeq 0}Lambda_i$ is a Koszul algebra with $Lambda_0$ isomorphic to a product of copies of a field, then the minimal projective resolution of $Lambda_0$ as a right $Lambda$-module provides all the information necessary to construct both a minimal projective resolution of $Lambda_0$ as a left $Lambda$-module and a minimal projective resolution of $Lambda$ as a right module over the enveloping algebra of $Lambda$. The main tool for this is showing that there is a comultiplicative structure on a minimal projective resolution of $Lambda_0$ as a right $Lambda$-module. | | Source: | arXiv, math.RA/0409162 | | Services: | Forum | Review | PDF | Favorites | |
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