On twisted group algebras of OTP representation type

2012 ◽  
Vol 127 (2) ◽  
pp. 213-232 ◽  
Author(s):  
Leonid F. Barannyk ◽  
Dariusz Klein
Keyword(s):  
Representation Type ◽  
Group Algebras ◽  
Twisted Group

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

Twisted group algebras I

1969 ◽  
Vol 13 (2) ◽  
pp. 119-130 ◽  
Author(s):  
C. M. Edwards ◽  
J. T. Lewis
Keyword(s):  
Group Algebras ◽  
Twisted Group

scholarly journals EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS

2011 ◽  
Vol 10 (05) ◽  
pp. 995-1106 ◽  
Author(s):  
MARIE-CLAUDE DAVID ◽  
NICOLAS M. THIÉRY
Keyword(s):  
Automorphism Groups ◽  
Group Algebras ◽  
Self Duality ◽  
Finite Dimensional ◽  
Twisted Group ◽  
Galois Correspondence ◽  
Index 2 ◽  
Original Motivation ◽  
The Way

We study the four infinite families KA(n), KB(n), KD(n), and KQ(n) of finite-dimensional Hopf (in fact Kac) algebras constructed, respectively, by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal sub-algebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we describe.

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