Some generalizations of preprojective algebras and their properties

详细信息    查看全文

• 作者：Louis de Thanhoffer de Volcsey ; ^{louis.dethanhofferdevolcsey@utoronto.ca" class="auth_mail" title="E-mail the corresponding author} ; Dennis Presotto ; ^{dennis.presotto@uhasselt.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Non-commutative algebras ; Preprojective algebras
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：470
• 期：Complete
• 页码：450-483
• 全文大小：536 K

文摘

In this note we consider a notion of relative Frobenius pairs of commutative rings 1" class="mathmlsrc">1-s2.0-S002186931630357X&_mathId=si1.gif&_user=111111111&_pii=S002186931630357X&_rdoc=1&_issn=00218693&md5=2401681bab2aa2c2ab504151551b6860" title="Click to view the MathML source">S/R. To such a pair, we associate an 1-s2.0-S002186931630357X&_mathId=si2.gif&_user=111111111&_pii=S002186931630357X&_rdoc=1&_issn=00218693&md5=c55740da3507d8834266bad420991608" title="Click to view the MathML source">N$\mathbb{N}$-graded R  -algebra 1-s2.0-S002186931630357X&_mathId=si29.gif&_user=111111111&_pii=S002186931630357X&_rdoc=1&_issn=00218693&md5=8820b053dd315680e0d277c704a35427" title="Click to view the MathML source">Π_R(S)${\mathrm{\Pi }}_R(S)$ which has a simple description and coincides with the preprojective algebra of a quiver with a single central node and several outgoing edges in the split case. If the rank of S over R is 4 and R   is Noetherian, we prove that 1-s2.0-S002186931630357X&_mathId=si29.gif&_user=111111111&_pii=S002186931630357X&_rdoc=1&_issn=00218693&md5=8820b053dd315680e0d277c704a35427" title="Click to view the MathML source">Π_R(S)${\mathrm{\Pi }}_R(S)$ is itself Noetherian and finite over its center and that each 1-s2.0-S002186931630357X&_mathId=si4.gif&_user=111111111&_pii=S002186931630357X&_rdoc=1&_issn=00218693&md5=7ae366cd346a1e5921c473f9192aff37" title="Click to view the MathML source">Π_R(S)_d${\mathrm{\Pi }}_R{(S)}_d$ is finitely generated projective. We also prove that 1-s2.0-S002186931630357X&_mathId=si29.gif&_user=111111111&_pii=S002186931630357X&_rdoc=1&_issn=00218693&md5=8820b053dd315680e0d277c704a35427" title="Click to view the MathML source">Π_R(S)${\mathrm{\Pi }}_R(S)$ is of finite global dimension if R and S are regular.