Minimal identities of symmetric matrices
Authors:
Wen Xin Ma and Michel L. Racine
Journal:
Trans. Amer. Math. Soc. 320 (1990), 171192
MSC:
Primary 16A38; Secondary 17C05
MathSciNet review:
961598
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Abstract: Let denote the subspace of symmetric matrices of , the full matrix algebra with coefficients in a field . The subspace does not have any polynomial identity of degree less than . Let , and if is even, if is odd. For all is an identity of . If the characteristic of does not divide and if , then any homogeneous polynomial identity of of degree is a consequence of . The case is also dealt with. The proofs are algebraic, but an equivalent formulation of the first result in graphtheoretical terms is given.
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 B. D. Smith, A standard Jordan polynomial, Comm. Algebra 5 (1977), 207218. MR 0430012 (55:3020)
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 Richard G. Swan, An application of graph theory to algebra, Proc. Amer. Math. Soc. 14 (1963), 367373; Correction, Proc. Amer. Math. Soc. 21 (1969), 379380. MR 0149468 (26:6956)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199009615986
PII:
S 00029947(1990)09615986
Article copyright:
© Copyright 1990
American Mathematical Society
