2020/09/05 by Plamen Koshlukov, Koshlukov, Plamen, Diogo Diniz P. S. Silva +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Sphingolipid Metabolism and Signaling #Advanced Topics in Algebra #Electron Spin Resonance Studies
paper · pdf · doi:10.48550/arxiv.2009.02530
The Jordan algebra of the symmetric matrices of order two over a field K\nhas two natural gradings by \ℤ2, the cyclic group of order 2. We\ndescribe the graded polynomial identities for these two gradings when the base\nfield is infinite and of characteristic different from 2. We exhibit bases for\nthese identities in each of the two cases. In one of the cases we perform a\nseries of computations in order to reduce the problem to dealing with\nassociators while in the other case one employs methods and results from\nInvariant theory. Moreover we extend the latter grading to a\n\ℤ2-grading on Bn, the Jordan algebra of a symmetric bilinear\nform in a vector space of dimension n (n=1, 2, \…, \∞). We call\nthis grading the \scalar one since its even part consists only of the\nscalars. As a by-product we obtain finite bases of the \ℤ2-graded\nidentities for Bn. In fact the last result describes the weak Jordan\npolynomial identities for the pair (Bn, Vn).\n