scholarly journals Induction formulae for Mackey functors with applications to representations of the twisted quantum double of a finite group

2014 ◽  
Vol 410 ◽  
pp. 85-147 ◽  
Author(s):  
Yugen Takegahara
Keyword(s):  
Finite Group ◽  
Quantum Double ◽  
Mackey Functors ◽  
A Finite Group

scholarly journals The dominant dimension of cohomological Mackey functors

2018 ◽  
Vol 17 (12) ◽  
pp. 1850228
Author(s):  
Markus Linckelmann
Keyword(s):  
Finite Group ◽  
Defect Group ◽  
Dominant Dimension ◽  
Text Block ◽  
Symmetric Algebras ◽  
Endomorphism Algebras ◽  
Mackey Functors ◽  
A Finite Group

We show that a separable equivalence between symmetric algebras preserves the dominant dimensions of certain endomorphism algebras of modules. We apply this to show that the dominant dimension of the category [Formula: see text] of cohomological Mackey functors of a [Formula: see text]-block [Formula: see text] of a finite group with a nontrivial defect group is [Formula: see text].

scholarly journals Quantum double finite group algebras and their representations

1993 ◽  
Vol 48 (2) ◽  
pp. 275-301 ◽  
Author(s):  
M.D. Gould
Keyword(s):  
Finite Group ◽  
Explicit Construction ◽  
Unitary Representations ◽  
Group Algebras ◽  
Baxter Equation ◽  
Irreducible Matrix ◽  
Matrix Representations ◽  
Quantum Double ◽  
Induced Representations ◽  
A Finite Group

The quantum double construction is applied to the group algebra of a finite group. Such algebras are shown to be semi-simple and a complete theory of characters is developed. The irreducible matrix representations are classified and applied to the explicit construction of R-matrices: this affords solutions to the Yang-Baxter equation associated with certain induced representations of a finite group. These results are applied in the second paper of the series to construct unitary representations of the Braid group and corresponding link polynomials.

The quantum double of a finite group and its role in conformal field theory

2010 ◽  
pp. 405-417 ◽  
Author(s):  
G Mason ◽  
C. M. Campbell ◽  
E. F. Robertson ◽  
T. C. Hurley ◽  
S. J. Tobin ◽  
...  
Keyword(s):  
Field Theory ◽  
Finite Group ◽  
Conformal Field Theory ◽  
Quantum Double ◽  
Conformal Field ◽  
A Finite Group

The Representation Ring and the Centre of a Hopf Algebra

1999 ◽  
Vol 51 (4) ◽  
pp. 881-896 ◽  
Author(s):  
Sarah J. Witherspoon
Keyword(s):  
Finite Group ◽  
Hopf Algebra ◽  
Character Table ◽  
Quantum Double ◽  
Representation Ring ◽  
Finite Dimensional ◽  
Dual Character ◽  
Structure Constants ◽  
A Finite Group ◽  
Cocommutative Hopf Algebra

AbstractWhen H is a finite dimensional, semisimple, almost cocommutative Hopf algebra, we examine a table of characters which extends the notion of the character table for a finite group. We obtain a formula for the structure constants of the representation ring in terms of values in the character table, and give the example of the quantum double of a finite group. We give a basis of the centre of H which generalizes the conjugacy class sums of a finite group, and express the class equation of H in terms of this basis. We show that the representation ring and the centre of H are dual character algebras (or signed hypergroups).

The Representation Ring of the Twisted Quantum Double of a Finite Group

1996 ◽  
Vol 48 (6) ◽  
pp. 1324-1338 ◽  
Author(s):  
S. J. Witherspoon
Keyword(s):  
Finite Group ◽  
Group Algebras ◽  
Quantum Double ◽  
Grothendieck Ring ◽  
Representation Ring ◽  
Twisted Group ◽  
A Finite Group

AbstractWe provide an isomorphism between the Grothendieck ring of modules of the twisted quantum double of a finite group, and a product of centres of twisted group algebras of centralizer subgroups. It follows that this Grothendieck ring is semisimple. Another consequence is a formula for the characters of this ring in terms of representations of twisted group algebras of centralizer subgroups.

scholarly journals Fourier transform and the Verlinde formula for the quantum double of a finite group

1999 ◽  
Vol 32 (48) ◽  
pp. 8539-8549 ◽  
Author(s):  
T H Koornwinder ◽  
B J Schroers ◽  
J K Slingerland ◽  
F A Bais
Keyword(s):  
Fourier Transform ◽  
Finite Group ◽  
Quantum Double ◽  
Verlinde Formula ◽  
A Finite Group

INVARIANTS OF 3-MANIFOLDS DERIVED FROM FINITE DIMENSIONAL HOPF ALGEBRAS

1995 ◽  
Vol 04 (01) ◽  
pp. 131-162 ◽  
Author(s):  
LOUIS H. KAUFFMAN ◽  
DAVID E. RADFORD
Keyword(s):  
Finite Group ◽  
Fundamental Group ◽  
Hopf Algebras ◽  
Quantum Double ◽  
Finite Dimensional ◽  
A Finite Group ◽  
The Given

This paper studies invariants of 3-manifolds derived from certain finite dimensional Hopf algebras via regular isotopy invariants of unoriented links in the blackboard framing. The invariants are based on right integrals for these Hopf algebras. It is shown that the resulting class of invariants is definitely distinct from the class of Witten-Reshetikhin-Turaev invariants. The invariant associated with the quantum double of a finite group G is treated in this context, and is shown to count the number of homomorphisms of the fundamental group of the 3-manifold to the given finite group G.

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