Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Abstract
2010 Mathematics Subject Classification: 16R10, 16R99, 16W50.Let K be an infinite field and let M2(K) be the matrix algebra of
order two over K. The polynomial identities of M2(K) are known whenever
the characteristic of K is different from 2. The algebra M2(K) admits a
natural grading by the cyclic group of order 2; the graded identities for
this grading are known as well. But M2(K) admits other gradings that
depend on the field and on its characteristic. Here we describe the graded
identities for all nontrivial gradings by the cyclic group of order 2 when the
characteristic of K equals 2. It turns out that there is only one grading to
consider. This grading is not elementary. On the other hand the graded
identities are the same as for the elementary grading.∗ Partially supported by grants from CNPq (No. 304003/2011-5), and from FAPESP (No. 2010/50347-9)
