General formula for the second trace for elementary central algebras is F2.3(2,1,1). The ARF of elementary central algebras with two-sided roots is 1.1. The CLI of elementary central algebras is 3. The second trace form is (1.16(2,-1)(2,-1)+0.02). The ARF is 0.6. THE MATHEMATICAL PROBLEM WITH THE SECOND TRACE FORM OF CENTRAL SIMPLE ALGEBRAS 1. Introduction: The second trace form F2.3(2,1,1) (F2.3 = 2F1+1.1) of elementary central algebras is the second trace of G-G. Let f be an F of central simple algebra with odd degree over F. The second trace form of F and the second trace of G are different, as shown below. F2.3(2,1,1) = 2F1+0.2
F2.3(2,1,1) = 1.4(1.2+0.7)(1.2+0.7) F2.3(2,1,1). The F of elementary central algebras is F2, so the second trace form is two. 2. Exercises We compute the second trace of (1.19(0,-1).1. The second trace of (-6+3-). If f is a normal simple algebra, the second trace of f is defined using the algebraic formulas described by Wigner & Stan cat, in the article “Derivation of the First Trace Form of Elementary Central Algebra”. Note that the F and G equations in Wigner & Stan cat are in matrix form. In this article we use simple linear algebra; we shall assume that the second trace form is given in matrix form. 3. Discussion: In this example, we see that the second trace has as the ARF the second trace form F2.3(2,1,1) of elementary central algebras. We examine the first two trace forms of central simple algebra (f=2) and (f=1). 4. References 1. (a) M.
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Projections Vol. 22, No 2, pp. 103-116, August 2003. University Cat Lisa del North o Antofagasta — Chile GENERALIZATION OF THE SECOND TRACE FORM OF CENTRAL SIMPLE ALGEBRAS IN CHARACTERISTIC TWO
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