Additive maps on rank K bivectors

Chooi, Wai Leong and Kwa, Kiam Heong (2020) Additive maps on rank K bivectors. Electronic Journal of Linear Algebra, 36. pp. 847-856. ISSN 1537-9582,

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Let u and v be linear spaces over fields F and K, respectively, such that dim u = n >= 2 and vertical bar F vertical bar >= 3. Let Lambda(2) u be the second exterior power of u. Fixing an even integer k satisfying n-1/2 <= k <= n, it is shown that a map psi: Lambda(2) u -> Lambda(2) v satisfies psi(u + v) = psi(u) + psi(v) for all rank k bivectors u, v is an element of Lambda(2) u if and only if psi is an additive map. Examples showing the indispensability of the assumption on k are given.

Item Type: Article
Funders: FRGS Research Grant Scheme (FRGS/1/2019/STG06/UM/02/1)
Uncontrolled Keywords: Additive maps; Second exterior powers; Bivectors; Ranks; Alternate matrices
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms Zaharah Ramly
Date Deposited: 31 May 2023 06:22
Last Modified: 31 May 2023 06:22

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