JOURNAL ARTICLE

The dual vector spaces of symmetric tensor powers of composition algebras.

  • Published In: Journal of Algebra & Its Applications, 2025, v. 24, n. 12. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Razon, Aharon 3 of 3

Abstract

Let be a quaternion algebra or an octonion algebra over a field F of characteristic 0. In a previous work, we show that the n th symmetric power Sym n of is isomorphic to a direct sum of central simple algebras m (n) , m = ⌈ n 2 ⌉ , ... , n. In this work, we study the dual vector spaces of the m (n) 's. We show that ( m (n) ) ∗ ≅ Sym 2 m − n ( ∗) μ n − m / Sym 2 m − n − 2 ( ∗) μ n − m + 1 , under the isomorphism induced by the isomorphism ( ⊗ n) ∗ ≅ ( ∗) ⊗ n , where μ ∈ ( ∗) ⊗ 2 = ( ⊗ 2) ∗ is the F -linear map ⊗ → F defined by μ (a ⊗ b) = Ntr (a ̄ b) for a , b ∈ , with Ntr and ¯ being the normalized trace and involution, respectively, of . [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Algebra & Its Applications. 2025/10, Vol. 24, Issue 12, p1
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2025
  • ISSN:0219-4988
  • DOI:10.1142/S0219498825502779
  • Accession Number:185309020
  • Copyright Statement:Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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