Computational aspects of Burnside rings part II: important maps

Kreuzer, M and Patil, DP (2020) Computational aspects of Burnside rings part II: important maps. In: Beitrage zur Algebra und Geometrie .

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Abstract

The Burnside ring B(G) of a finite group G, a classical tool in the representation theory of finite groups, is studied from the point of view of computational algebra. In the first part (cf. Kreuzer and Patil, Beitr Algebra Geom 58:427�452, 2017) we examined the ring theoretic properties of B(G) using the methods of computer algebra. In this part we shift our focus to important maps between two Burnside rings and make several well-known maps of representation theory explicitly computable. The inputs of all our algorithms are the tables of marks of the two groups, and the outputs are matrices of integers representing the maps via their image in the ghost ring. All algorithms have been implemented in the computer algebra system ApCoCoA and are illustrated by applying them to explicit examples. Especially, we study the restriction and induction maps, the projection and inflation maps, the conjugation isomorphism, and the Frobenius-Wielandt homomorphism. © 2020, The Managing Editors.

Item Type:	Journal Article
Publication:	Beitrage zur Algebra und Geometrie
Publisher:	Springer
Additional Information:	The copyright of this article belongs to Springer
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	11 Sep 2020 11:47
Last Modified:	11 Sep 2020 11:47
URI:	http://eprints.iisc.ac.in/id/eprint/66502

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