Dimensions of anisotropic indefinite quadratic forms. I.
Hoffmann, Detlev W. (2001)
Documenta Mathematica
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Displaying similar documents to “Excellent special orthogonal groups.”
Dimensions of anisotropic indefinite quadratic forms. I.
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The algebras ℂ (complex numbers), ℍ (quaternions), and 𝕆 (octonions) are real division algebras obtained from the real numbers ℝ by a doubling procedure called the Cayley-Dickson Process. By doubling ℝ (dim 1), we obtain ℂ (dim 2), then ℂ produces ℍ (dim 4), and ℍ yields 𝕆 (dim 8). The next doubling process applied to 𝕆 then yields an algebra 𝕊 (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra 𝕊 and its zero divisors. In particular,...
Some seminorms on quasi *-algebras
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Different types of seminorms on a quasi *-algebra (𝔄,𝔄₀) are constructed from a suitable family ℱ of sesquilinear forms on 𝔄. Two particular classes, extended C*-seminorms and CQ*-seminorms, are studied in some detail. A necessary and sufficient condition for the admissibility of a sesquilinear form in terms of extended C*-seminorms on (𝔄,𝔄₀) is given.