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On the representation theory of braid groups

Ivan Marin (2013)

Annales mathématiques Blaise Pascal

This work presents an approach towards the representation theory of the braid groups B n . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures on classical...

On the structure of the augmentation quotient group for some nonabelian 2-groups

Jizhu Nan, Huifang Zhao (2012)

Czechoslovak Mathematical Journal

Let G be a finite nonabelian group, G its associated integral group ring, and ( G ) its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups Q n ( G ) = n ( G ) / n + 1 ( G ) is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .

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