NDLI: The Higher Relation Bimodule

Content Provider	Springer Nature Link
Author	Assem, Ibrahim Gatica, Maria Andrea Schiffler, Ralf
Copyright Year	2012
Abstract	Given a finite dimensional algebra A of finite global dimension, we consider the trivial extension of A by the A − A-bimodule $\oplus_{i\ge 2} {\rm Ext}^i_A(DA,A)$ , which we call the higher relation bimodule. We first give a recipe allowing to construct the quiver of this trivial extension in case A is a string algebra and then apply it to prove that, if A is gentle, then the tensor algebra of the higher relation bimodule is gentle.
Ending Page	999
Page Count	21
Starting Page	979
File Format	PDF
ISSN	1386923X
e-ISSN	15729079
Journal	Algebras and Representation Theory
Issue Number	4
Volume Number	16
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-05-27
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Associative Rings and Algebras Relation extension String algebra Representations of quivers and partially ordered sets Non-associative Rings and Algebras Trivial extension Cluster algebras Commutative Rings and Algebras Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers Resolution
Content Type	Text
Resource Type	Article
Subject	Mathematics

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The Higher Relation Bimodule