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Eulerian Graphs and Polynomial Identities for Skew-Symmetric Matrices

Published online by Cambridge University Press:  20 November 2018

Joan P. Hutchinson
Joan P. Hutchinson*
Affiliation:
Dartmouth College, Hanover, New Hampshire
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Let the standard identity of degree m be given by

Then we shall show that the set of all n X n skew-symmetric matrices over a field of characteristic 0 satisfies the standard identity of degree at least 2n — 2; specifically, we shall prove the following.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 590 - 609
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Amitsur, S. A. and Levitzki, J., Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449–463.Google Scholar
2. Hutchinson, J. P., Eulerian graphs and polynomial identities for sets of matrices, Proc. Nat. Acad. Sci. U.S.A. 77(1974), 1314–1316.Google Scholar
3. Kostant, B., A theorem of Frobenius, a theorem of Amitsur-Levitzki, and cohomology theory, J. Math. Mech. 7 (1958), 237–264.Google Scholar
4. Kumin, H. G. and Smith, K. C., Identities on matrices, Amer. Math. Monthly 79 (1972), 157–158.Google Scholar
5. Owen, F. W., Graph theory and identities on matrices, Notices Amer. Math. Soc. 20 (1973), A-35.Google Scholar
6. Rowen, L. H., Standard identities for matrix rings with involution, Notices Amer. Math. Soc. 20 (1973), A-76.Google Scholar
7. Swan, R. G., An application of graph theory to algebra, Proc. Amer. Math. Soc 14 (1963), 367–373.Google Scholar
8. Swan, R. G., Correction to “An application of graph theory to algebra”, Proc. Amer. Math. Soc. 21 (1969), 379–380.Google Scholar