Gelfand-Kirillov dimensions of simple modules over twisted group algebras [IMG align=ABSMIDDLE alt=$ k*a$]tex_im_3109_img1[/IMG]

2022 ◽  
Vol 86 (3) ◽  
Author(s):  
Ashish Gupta ◽  
Umamaheswaran Arunachalam
Keyword(s):  
Group Algebras ◽  
Simple Modules ◽  
Twisted Group

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.

scholarly journals Minimal Idempotents of Twisted Group Algebras of Cyclic 2-Groups

2003 ◽  
Vol 26 (4) ◽  
pp. 593-601
Author(s):  
Todor Zh. Mollov ◽  
Nako A. Nachev
Keyword(s):  
Group Algebras ◽  
Twisted Group

scholarly journals On Units of Twisted Group Algebras

2002 ◽  
Vol 250 (1) ◽  
pp. 271-282 ◽  
Author(s):  
Chia-Hsin Liu
Keyword(s):  
Group Algebras ◽  
Twisted Group

scholarly journals On blocks of twisted group algebras

1985 ◽  
Vol 14 (2) ◽  
pp. 155-162 ◽  
Author(s):  
G. KARPILOVSKY
Keyword(s):  
Group Algebras ◽  
Twisted Group

scholarly journals Closure operations and group algebras

1972 ◽  
Vol 18 (2) ◽  
pp. 149-158 ◽  
Author(s):  
J. D. P. Meldrum ◽  
D. A. R. Wallace
Keyword(s):  
Vector Space ◽  
Associative Algebra ◽  
Group Algebra ◽  
Jacobson Radical ◽  
Group Algebras ◽  
Twisted Group Algebra ◽  
Twisted Group ◽  
Closure Operations ◽  
Image Position

Let G be a group and let K be a field. The twisted group algebra Kt(G) of G over K is defined as follows: let G have elements a, b, c, … and let Kt(G) be the vector space over K with basis elements ; let α: G ×G → K be a 2-cocycle and define a multiplication on Kt(G) byextending this by linearity to Kt(G) yields an associative algebra. We are interested in information concerning the Jacobson radical of Kt(G), denoted by JKt(G).

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