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Additive maps on rank K bivectors

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...

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Main Authors: Chooi, Wai Leong, Kwa, Kiam Heong
Format: Article
Published: Int Linear Algebra Soc 2020
Subjects:
QA Mathematics
Online Access:http://eprints.um.edu.my/37094/
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spelling my.um.eprints.370942023-05-31T06:22:47Z http://eprints.um.edu.my/37094/ Additive maps on rank K bivectors Chooi, Wai Leong Kwa, Kiam Heong QA Mathematics 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. Int Linear Algebra Soc 2020-12 Article PeerReviewed 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,
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Chooi, Wai Leong
Kwa, Kiam Heong
Additive maps on rank K bivectors
description 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.
format Article
author Chooi, Wai Leong
Kwa, Kiam Heong
author_facet Chooi, Wai Leong
Kwa, Kiam Heong
author_sort Chooi, Wai Leong
title Additive maps on rank K bivectors
title_short Additive maps on rank K bivectors
title_full Additive maps on rank K bivectors
title_fullStr Additive maps on rank K bivectors
title_full_unstemmed Additive maps on rank K bivectors
title_sort additive maps on rank k bivectors
publisher Int Linear Algebra Soc
publishDate 2020
url http://eprints.um.edu.my/37094/
_version_ 1768007308531466240
score 13.211869

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