nakayama algebra - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T06:41:26Z http://mathoverflow.net/feeds/question/88005 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88005/nakayama-algebra nakayama algebra paria 2012-02-09T16:24:21Z 2012-02-09T16:56:37Z <p>Let A be a self-injective connected Nakayama algebra.what is the Loewy length of any indecomposable projective A-module?</p> http://mathoverflow.net/questions/88005/nakayama-algebra/88010#88010 Answer by Julian Kuelshammer for nakayama algebra Julian Kuelshammer 2012-02-09T16:56:37Z 2012-02-09T16:56:37Z <p>The Loewy length can be arbitrary. See e.g. [Assem, Simson, Skowronski: Elements of the Representation Theory of Associative Algebras 1] Proposition V.3.8:</p> <blockquote> <p>\$A\$ basic, self-injective, connected Nakayama, then \$A\cong kQ/I\$, where \$Q\$ is an oriented cycle and \$I=(kQ^+)^h\$, where \$(kQ^+)\$ is the ideal spanned by all the arrows.</p> </blockquote> <p>The Loewy length of each projective indecomposable should then be \$h\$.</p> <p>This certainly also holds true for non-basic algebras if you replace isomorphism by Morita equivalence.</p>