scholarly journals Finite-dimensional twisted group algebras of semi-wild representation type

2010 ◽  
Vol 120 (2) ◽  
pp. 277-298 ◽  
Author(s):  
Leonid F. Barannyk
Keyword(s):  
Representation Type ◽  
Group Algebras ◽  
Finite Dimensional ◽  
Twisted Group ◽  
Wild Representation Type

CLOSE NEIGHBORS IN THE QUIVER OF TILTING MODULES

2008 ◽  
Vol 07 (03) ◽  
pp. 379-392
Author(s):  
DIETER HAPPEL
Keyword(s):  
Representation Type ◽  
Tilting Module ◽  
Tilting Modules ◽  
Hereditary Algebra ◽  
Simple Modules ◽  
Finite Dimensional ◽  
Wild Representation Type ◽  
Local Properties

For a finite dimensional hereditary algebra Λ local properties of the quiver [Formula: see text] of tilting modules are investigated. The existence of special neighbors of a given tilting module is shown. If Λ has more than 3 simple modules it is shown as an application that Λ is of wild representation type if and only if [Formula: see text] is a subquiver of [Formula: see text].

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.

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

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Fields of Definition for Representations of Associative Algebras

2018 ◽  
Vol 62 (1) ◽  
pp. 291-304
Author(s):  
Dave Benson ◽  
Zinovy Reichstein
Keyword(s):  
Finite Extension ◽  
Representation Type ◽  
Essential Dimension ◽  
Extension Field ◽  
Associative Algebras ◽  
Separable Extension ◽  
Finite Representation ◽  
Field Of Definition ◽  
Finite Dimensional ◽  
A Finite Group

AbstractWe examine situations, where representations of a finite-dimensionalF-algebraAdefined over a separable extension fieldK/F, have a unique minimal field of definition. Here the base fieldFis assumed to be a field of dimension ≼1. In particular,Fcould be a finite field ork(t) ork((t)), wherekis algebraically closed. We show that a unique minimal field of definition exists if (a)K/Fis an algebraic extension or (b)Ais of finite representation type. Moreover, in these situations the minimal field of definition is a finite extension ofF. This is not the case ifAis of infinite representation type orFfails to be of dimension ≼1. As a consequence, we compute the essential dimension of the functor of representations of a finite group, generalizing a theorem of Karpenko, Pevtsova and the second author.

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