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Existence of an invariant form under a linear map

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Abstract

Let F be a field of characteristic different from 2 and V be a vector space over F. Let J: α → α J be a fixed involutory automorphism on F. In this paper we answer the following question: given an invertible linear map T: V → V, when does the vector space V admit a T-invariant nondegenerate J-hermitian, resp. J-skew-hermitian, form?

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Authors and Affiliations

  1. Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S.A.S. Nagar, Punjab, 140 306, India

    Krishnendu Gongopadhyay

  2. Department of Mathematics, Jadavpur University, Jadavpur, Kolkata, 700 032, India

    Sudip Mazumder

Authors
  1. Krishnendu Gongopadhyay
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  2. Sudip Mazumder
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Correspondence to Krishnendu Gongopadhyay.

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Gongopadhyay, K., Mazumder, S. Existence of an invariant form under a linear map. Indian J Pure Appl Math 48, 211–220 (2017). https://doi.org/10.1007/s13226-017-0222-y

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  • DOI: https://doi.org/10.1007/s13226-017-0222-y

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