Research Statement Oleg N. Smirnov
نویسنده
چکیده
1.1 Graded associative algebras. A nite Z-grading of an algebra A is a decomposition A = L n i=?n A i such that A i A j A i+j , where A i = 0 for jij > n. From now on a grading means a nite Z-grading. I am interested in associative graded algebras because they arise naturally in study of Lie algebras, although the subject is certainly interesting in its own right. A classiication of gradings of simple artinian associative algebras was provided by NN astt asescu and Van Oystaen (see 18]). In 33] I obtained a description of gradings of simple and involutary simple associative algebras. For a unital simple algebra R it looks as follows: for any grading
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