On quasi-commutative matrices

McCoy, Neal H.

doi:10.1090/s0002-9947-1934-1501746-8

Cited by 30 publications

(23 citation statements)

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“…Certain of our results (Theorems 1,3,4) are close to known results in the theory of Lie algebras. Nevertheless, we present full proofs.…”

supporting

confidence: 85%

“…This completes the proof of Theorem 9 (and also of Theorem 6). THEOREM It should be pointed out that much of the argument of § 4 is very close to arguments first found by McCoy [4], 5* The number of similarity classes of commutators• In §5 only, we let p(n) denote the number of partitions of n and p\n) denote the number of partitions of n into distinct summands. THEOREM …”

Section: This Proves Theorem 5 (I)mentioning

confidence: 70%

“…Question II has already been examined by McCoy [4] when K is the complex number field. In our discussion of Question II, we obtain results that partially duplicate and partially complement McCoy's results.…”

mentioning

confidence: 99%

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On a class of matrix equations

Thompson¹

1967

Pacific J. Math.

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“…Certain of our results (Theorems 1,3,4) are close to known results in the theory of Lie algebras. Nevertheless, we present full proofs.…”

supporting

confidence: 85%

Section: This Proves Theorem 5 (I)mentioning

confidence: 70%

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On a class of matrix equations

Thompson¹

1967

Pacific J. Math.

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“…Property 3 does not imply property 4 even for n = 2. Property 4 does not imply property 5 for re>2 (see [3]). That property 5 does not imply property 6 is well known, see e.g.…”

Section: Quasi-commutativitymentioning

confidence: 99%

Pairs of matrices with property 𝐿

Motzkin¹,

Taussky²

1952

Trans. Amer. Math. Soc.

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“…In this case we have the following result. This implies that (6) v2u -v(vu) = v, uh -u(uv) = u and that v is nilpotent.…”

mentioning

confidence: 95%

Operator Commutativity in Jordan Algebras

Jacobson¹

1952

Proceedings of the American Mathematical Society

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If a and b are elements of a Jordan algebra 31 we say that a and b operator-commute or o-commute if the multiplications Ra and 7?¡, commute. Here Ra is the linear transformation x->xa = ax of 21. The notion of o-commutativity has been introduced by Jordan, Wigner, and von Neumann [4] who called this concept simply commutativity. Since every Jordan algebra is commutative in the usual sense, the above change in terminology seems to be desirable. In this note we shall study the notion of o-commutativity for finite-dimensional Jordan algebras of characteristic 0. Our results are based on those of two previous papers [l; 2].1. If S3 is a subset of the Jordan algebra 21, then we denote by Sa(33) the subset of 21 of elements which o-commute with every ÔGS3. Evidently (Sa(33) is a subspace of 21, but, as we shall see presently, it is not always a subalgebra. Assume now that 21 is a special Jordan algebra, that is, 21 is a subspace of an associative algebra U closed relative to the Jordan multiplication {ab} = ab-+ba where ab now denotes the associative multiplication. We can now construct an example in which Sa (58) is not an algebra. Let a, b, c be finite matrices such that In this note we shall consider Sa(33) such that either 21 or 53 is semisimple. Our first result is as follows: Theorem 1. Let 2Í be a special semi-simple finite-dimensional Jordan

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On quasi-commutative matrices

Cited by 30 publications

References 0 publications

On a class of matrix equations

On a class of matrix equations

Pairs of matrices with property 𝐿

Operator Commutativity in Jordan Algebras

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