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Title: Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2
Authors: Koshlukov, Plamen
César dos Reis, Júlio
Keywords: Gradings on Matrix Algebras
Graded Identities
Polynomial Identities in characteristic two
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 189p-198p
Abstract: 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.
Description: 2010 Mathematics Subject Classification: 16R10, 16R99, 16W50.
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

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