Evaluations of noncommutative polynomials on algebras: Methods and problems, and the L'vov-Kaplansky Conjecture

Kanel-Belov, A.; Malev, S.; Rowen, L.; Yavich, R.

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 24 сентября 2020 г.

Авторы: Alexei Kanel-Belov, Sergey Malev, Louis Rowen, Roman Yavich
Журнал: Symmetry, Integrability and Geometry - Methods and Applications
Том: 16
Год издания: 2020
Издательство: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
Местоположение издательства: Ukraine
Номер статьи: 071
DOI: 10.3842/SIGMA.2020.071
Аннотация: Let $p$ be a polynomial in several non-commutingvariables with coefficients in an algebraically closed field $K$ ofarbitrary characteristic. It has been conjectured that for any $n$,for $p$ multilinear, theimage of $p$ evaluated on the set $M_n(K)$ of $n$ by $n$ matricesis either zero, or the set of scalar matrices, or the set$\ssl_n(K)$ of matrices of trace 0, or all of $M_n(K)$.This expository paper describes research on this problem andrelated areas. We settle this conjecture for $n=2$ and obtaindecisive results for $n=3$, and partial information for $n\geq 3$,also for non-multilinear polynomials.In addition we consider the case of $K$ not algebraically closed,and polynomials evaluated on other finite dimensional simplealgebras (in particular the algebra of the quaternions).
Добавил в систему: Белов Алексей Яковлевич

	ИСТИНА	Войти в систему Регистрация
	ИСТИНА ЦЭМИ РАН
	Главная Поиск Статистика О проекте Помощь

ИСТИНА

ИСТИНА ЦЭМИ РАН

Evaluations of noncommutative polynomials on algebras: Methods and problems, and the L'vov-Kaplansky Conjectureстатья

Прикрепленные файлы