Additive maps on rank K bivectors
Document Type
Article
Publication Date
12-1-2020
Abstract
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.
Keywords
Additive maps, Second exterior powers, Bivectors, Ranks, Alternate matrices
Divisions
MathematicalSciences
Funders
FRGS Research Grant Scheme (FRGS/1/2019/STG06/UM/02/1)
Publication Title
Electronic Journal of Linear Algebra
Volume
36
Publisher
Int Linear Algebra Soc
Publisher Location
C/O JAMES WEAVER DEPT MATH & STATISTICS, UNIV WEST FLORIDA, 11000 UNIV PARKWAY, PENSACOLA, FLORIDA 32514-5751 USA