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A scalar expression for matrices with symplectic involution

Authors: Louis Halle Rowen and Uri Schild
Journal: Math. Comp. 32 (1978), 607-613
MSC: Primary 16A28; Secondary 16A42
MathSciNet review: 0480620
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Abstract: Various algebraic reductions are made to facilitate computer verification of the following result: If x and y are $ 8 \times 8$ matrices such that [x, y] is regular, $ \operatorname{tr} (x) = 0$ , and, with respect to the canonical symplectic involution, x is symmetric and y is antisymmetric, then the element $ {(x + [x,y]x{[x,y]^{ - 1}})^2}$ satisfies a minimal equation of degree $ \leqslant 2$.

References [Enhancements On Off] (What's this?)

  • [1] A. Adrian Albert, Structure of algebras, Revised printing. American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. MR 0123587
  • [2] Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0053905
  • [3] Thomas Muir, A treatise on the theory of determinants, Revised and enlarged by William H. Metzler, Dover Publications, Inc., New York, 1960. MR 0114826
  • [4] Louis Halle Rowen, Identities in algebras with involution, Israel J. Math. 20 (1975), 70–95. MR 0437585
  • [5] Louis Halle Rowen, Central simple algebras, Israel J. Math. 29 (1978), no. 2-3, 285–301. MR 0491810

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Article copyright: © Copyright 1978 American Mathematical Society