Skip Navigation

Journal of the London Mathematical Society 1999 59(1):76-86; doi:10.1112/S0024610799007036
© 1999 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Sköldberg, E.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

The Hochschild Homology of Truncated and Quadratic Monomial Algebras

Emil Sköldberg

Matematiska Institutionen, Stockholms Universitet S-106 91 Stockholm, Sweden

Received 3 May 1996. Revision received 16 July 1996.

Let {Delta} be a finite quiver, that is, a finite directed graph, k be a commutative ring, and k{Delta} be the semigroup ring of paths in {Delta}. In this paper we compute the Hochschild homology of the following classes of algebras:

(1) k{Delta}/mn, where m is the arrow ideal;

(2) k{Delta}/I where I is an ideal generated by quadratic monomials.

In Section 2 we establish the notation, and recall a projective resolution of k{Delta}0, the degree 0 part in k{Delta}, over a monomial algebra which is due to Anick and Green. This resolution is then used in Section 3 as the building block in the construction of a resolution of a truncated or quadratic monomial algebra A, over its enveloping algebra (in the Hochschild sense), Ae. The fact that a monomial algebra possesses a fine grading then enables us to compute the homology.

The results obtained extend results by Liu and Zhang [3] and Geller, Reid and Weibel [2].


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.