• Space of invariant bilinear forms

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/128/04/0047

• Keywords

Vector space; invariant bilinear forms; infinitesimal invariant forms

• Abstract

Let $\mathbb{F}$ be a field, $V$ a vector space of dimension $n$ over $\mathbb{F}$. Then the set of bilinear forms on $V$ forms a vector space of dimension $n^{2}$ over $\mathbb{F}$. For char $\mathbb{F} \neq 2$, if $T$ is an invertible linear map from $V$ onto $V$ then the set of $T$ -invariant bilinear forms, forms a subspace of this space of forms. In this paper, we compute the dimension of $T$ -invariant bilinear forms over $\mathbb{F}$. Also we investigate similar type of questions for the infinitesimally $T$ -invariant bilinear forms ($T$ -skew symmetric forms). Moreover, we discuss the existence of nondegenerate invariant (resp. infinitesimally invariant) bilinear forms.

• Author Affiliations

1. Bhaskaracharya Pratisthana, 56/14, Erandavane, Off Law College Road, Pune 411 004, India
2. Central University of Jharkhand, CTI Campus, Ratu-Lohardaga Road, Brambe, Ranchi 835 205, India

• Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019