scholarly journals Super cocommutative Hopf algebras of finite representation type

2012 ◽  
Vol 358 ◽  
pp. 128-142
Author(s):  
Gongxiang Liu
Keyword(s):  
Hopf Algebras ◽  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type

scholarly journals On the First Hochschild Cohomology of Cocommutative Hopf Algebras of Finite Representation Type

2020 ◽  
Vol 71 (3) ◽  
pp. 1131-1142
Author(s):  
Hao Chang
Keyword(s):  
Hopf Algebras ◽  
Hochschild Cohomology ◽  
Group Scheme ◽  
Representation Type ◽  
Closed Field ◽  
Algebra Structure ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Principal Block ◽  
Restricted Lie Algebra

Abstract Let $\mathscr{B}_0({\mathcal{G}})\subseteq k\,{\mathcal{G}}$ be the principal block algebra of the group algebra $k\,{\mathcal{G}}$ of an infinitesimal group scheme ${\mathcal{G}}$ over an algebraically closed field $k$ of characteristic ${\operatorname{char}}(k)=:p\geq 3$. We calculate the restricted Lie algebra structure of the first Hochschild cohomology ${\mathcal{L}}:={\operatorname{H}}^1(\mathscr{B}_0({\mathcal{G}}),\mathscr{B}_0({\mathcal{G}}))$ whenever $\mathscr{B}_0({\mathcal{G}})$ has finite representation type. As a consequence, we prove that the complexity of the trivial ${\mathcal{G}}$-module $k$ coincides with the maximal toral rank of ${\mathcal{L}}$.

Auslander algebras Of finite representation type

1987 ◽  
Vol 15 (1-2) ◽  
pp. 377-424 ◽  
Author(s):  
Kiyoshi Igusa ◽  
Maria-Ines Platzeck ◽  
Gordana Todorov ◽  
Dan Zachana
Keyword(s):  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type

Integer sequences arising from Auslander–Reiten quivers of some hereditary artin algebras

2020 ◽  
pp. 2150051
Author(s):  
Agustín Moreno Cañadas ◽  
Gabriel Bravo Rios ◽  
Hernán Giraldo
Keyword(s):  
Representation Type ◽  
Integer Sequences ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Artin Algebras

Categorification of some integer sequences are obtained by enumerating the number of sections in the Auslander–Reiten quiver of algebras of finite representation type.

Cycles of modules and finite representation type

2016 ◽  
Vol 48 (4) ◽  
pp. 589-600
Author(s):  
Jerzy Białkowski ◽  
Andrzej Skowroński
Keyword(s):  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type

Group algebras of finite representation type

1983 ◽  
Vol 182 (1) ◽  
pp. 129-148 ◽  
Author(s):  
Hagen Meltzer ◽  
Andrzej Skowroński
Keyword(s):  
Representation Type ◽  
Group Algebras ◽  
Finite Representation ◽  
Finite Representation Type
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