SPACE OF INVARIANT BILINEAR FORMS UNDER REPRESENTATION OF A GROUP OF ORDER 8


By

Dilchand Mahto and Jagmohan Tanti

Department of Mathematics, Central University of Jharkhand, Ranchi- 835205, Jharkhand, India

Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, Uttar Pradesh, India

Email:dilchandiitk@gmail.com, jagmohan.t@gmail.com

(Received : August 19, 2021; In format : September 18, 2021; Revised in final form : October 07, 2021)


DOI: https://doi.org/10.58250/Jnanabha.2021.51218

Abstract

Let G be a group of order 8 and F an algebraically closed field with char(F)≠2. In this paper we compute the number of n degree representations of G and subsequent dimensions of the corresponding spaces of invariant bilinear forms over the field F. We explicitly discuss about the existence of non-degenerate invariant bilinear forms.


2020 Mathematical Sciences Classification: 15A63; 20C15; 15A03.

Keywords and Phrases: Invariant bilinear forms ; Representation of groups; Vector spaces; Direct sums.




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