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      Permanent link:
      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

       

      RAVI S KULKARNI1 JAGMOHAN TANTI2

      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
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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