Kernels of representations of Drinfeld doubles of finite groups

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Sebastian Burciu
Keyword(s):  
Hopf Algebra ◽  
Finite Groups ◽  
Fusion Category ◽  
Semisimple Hopf Algebra ◽  
Normal Hopf Subalgebras

AbstractA description of the commutator of a normal subcategory of the fusion category of representation Rep A of a semisimple Hopf algebra A is given. Formulae for the kernels of representations of Drinfeld doubles D(G) of finite groups G are presented. It is shown that all these kernels are normal Hopf subalgebras.

scholarly journals Normal Hopf subalgebras in cocycle deformations of finite groups

2008 ◽  
Vol 125 (4) ◽  
pp. 501-514 ◽  
Author(s):  
César Galindo ◽  
Sonia Natale
Keyword(s):  
Finite Groups ◽  
Normal Hopf Subalgebras

scholarly journals Depth two Hopf subalgebras of a semisimple Hopf algebra

2009 ◽  
Vol 322 (1) ◽  
pp. 162-176 ◽  
Author(s):  
Sebastian Burciu ◽  
Lars Kadison
Keyword(s):  
Hopf Algebra ◽  
Semisimple Hopf Algebra

On Semisimple Hopf Algebras of Dimension pqn

2014 ◽  
Vol 57 (2) ◽  
pp. 264-269
Author(s):  
Li Dai ◽  
Jingcheng Dong
Keyword(s):  
Hopf Algebra ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Prime Numbers ◽  
Closed Field ◽  
Semisimple Hopf Algebra ◽  
Algebraically Closed Field

AbstractLet p, q be prime numbers with p2 < q, n ∊ ℕ, and H a semisimple Hopf algebra of dimension pqn over an algebraically closed field of characteristic 0. This paper proves that H must possess one of the following two structures: (1) H is semisolvable; (2) H is a Radford biproduct R#kG, where kG is the group algebra of group G of order p and R is a semisimple Yetter–Drinfeld Hopf algebra in of dimension qn.

Algebraic Structures Associated to Orbifold Wreath Products

2010 ◽  
Vol 8 (2) ◽  
pp. 323-338
Author(s):  
Carla Farsi ◽  
Christopher Seaton
Keyword(s):  
Hopf Algebra ◽  
Wreath Product ◽  
Finite Groups ◽  
Lie Group ◽  
Wreath Products ◽  
Closed Manifold ◽  
Algebraic Structures ◽  
Present Structure ◽  
Smooth Closed Manifold ◽  
Connected Lie Group

AbstractWe present structure theorems in terms of inertial decompositions for the wreath product ring of an orbifold presented as the quotient of a smooth, closed manifold by a compact, connected Lie group acting almost freely. In particular we show that this ring admits λ-ring and Hopf algebra structures both abstractly and directly. This generalizes results known for global quotient orbifolds by finite groups.

scholarly journals ON THREE-DIMENSIONAL TOPOLOGICAL FIELD THEORIES CONSTRUCTED FROM Dω(G) FOR FINITE GROUPS

1994 ◽  
Vol 09 (25) ◽  
pp. 2359-2369 ◽  
Author(s):  
MASAKO ASANO ◽  
SABURO HIGUCHI
Keyword(s):  
Partition Function ◽  
Hopf Algebra ◽  
Topological Field Theories ◽  
Finite Groups ◽  
Three Dimensional ◽  
Commutative Group ◽  
Field Theories ◽  
Quantum Double ◽  
Topological Field

We investigate the 3-D lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation Dω(G) of the quantum double of a finite commutative group G as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by Z CFS =|Z DW |2 when G=ℤ2N+1. For G=ℤ2N, such a relation does not hold.

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