Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2

Koshlukov, Plamen, and César dos Reis, Júlio. "Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2." Serdica Mathematical Journal 38.1-3 (2012): 189-198. <http://eudml.org/doc/288256>.

@article{Koshlukov2012,
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).},
author = {Koshlukov, Plamen, César dos Reis, Júlio},
journal = {Serdica Mathematical Journal},
keywords = {Gradings on Matrix Algebras; Graded Identities; Polynomial Identities in characteristic two},
language = {eng},
number = {1-3},
pages = {189-198},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2},
url = {http://eudml.org/doc/288256},
volume = {38},
year = {2012},
}

TY - JOUR
AU - Koshlukov, Plamen
AU - César dos Reis, Júlio
TI - Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2
JO - Serdica Mathematical Journal
PY - 2012
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 38
IS - 1-3
SP - 189
EP - 198
AB - 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).
LA - eng
KW - Gradings on Matrix Algebras; Graded Identities; Polynomial Identities in characteristic two
UR - http://eudml.org/doc/288256
ER -