Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class

Wreath Products in Modular Group Algebras of Some Finite 2-groups

Let K be field of characteristic 2 and let G be a finite nonabelian 2-group with the cyclic derived subgroup G′, and there exists a central element z of order 2 in Z(G)\G′. We prove that the unit group of the group algebra KG possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group G, giving for such groups a positive answer to the questi...

On the Representation Dimension of Skew Group Algebras, Wreath Products and Blocks of Hecke Algebras

We establish bounds for the representation dimension of skew group algebras and wreath products. Using this, we obtain bounds for the representation dimension of a block of a Hecke algebra of type A, in terms of the weight of the block. This includes certain blocks of group algebras of symmetric groups.

Reflection Functors and Symplectic Reflection Algebras for Wreath Products

We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit under the Weyl group action. We give applications to the representation theory of symplectic reflection algebras of wreath product groups.

A Class of Two Generated Automaton Groups on a Three Letter Alphabet

Vertex Algebras and the Class Algebras of Wreath Products

The Jucys-Murphy elements for wreath products Γn associated to any finite group Γ are introduced and they play an important role in our study on the connections between class algebras of Γn for all n and vertex algebras. We construct an action of (a variant of) the W1+∞ algebra acting irreducibly on the direct sum RΓ of the class algebras of Γn for all n in a group theoretic manner. We establis...