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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Institution:	Universiti Malaya

id	my.um.eprints.37094
record_format	eprints
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

Additive maps on rank K bivectors

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