ON SEMITRANSITIVE JORDAN ALGEBRAS OF MATRICES
2011 ◽
Vol 10
(02)
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pp. 319-333
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Keyword(s):
A set [Formula: see text] of linear operators on a vector space is said to be semitransitive if, given nonzero vectors x, y, there exists [Formula: see text] such that either Ax = y or Ay = x. In this paper we consider semitransitive Jordan algebras of operators on a finite-dimensional vector space over an algebraically closed field of characteristic not two. Two of our main results are: (1) Every irreducible semitransitive Jordan algebra is actually transitive. (2) Every semitransitive Jordan algebra contains, up to simultaneous similarity, the upper triangular Toeplitz algebra, i.e. the unital (associative) algebra generated by a nilpotent operator of maximal index.
Keyword(s):
1982 ◽
Vol 25
(2)
◽
pp. 133-139
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1970 ◽
Vol 22
(2)
◽
pp. 363-371
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2016 ◽
Vol 15
(09)
◽
pp. 1650159
Keyword(s):
1986 ◽
Vol 69
(4)
◽
pp. 37-46
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