Open AccessInfinite homogeneous algebras are anticommutative
Author(s) -
Dragomir Ž. Djoković,
Lowell Sweet
Publication year - 1999
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-99-04910-2
Subject(s) - algorithm , annotation , computer science , type (biology) , artificial intelligence , biology , ecology
A (non-associative) algebra A A , over a field k k , is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of A A . Suppose A A is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that x 2 = 0 x^{2}=0 for all x x in A A , and so x y = − y x xy=-yx for all x , y ∈ A x,y\in A .