Systems of linear equations equations over associative algebras and the occurrence problem for Lie algebras

Authors
Gupta, CK Umirbaev, UU
Citation
Ck. Gupta et Uu. Umirbaev, Systems of linear equations equations over associative algebras and the occurrence problem for Lie algebras, COMM ALGEB, 27(1), 1999, pp. 411-427
Citations number
15
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
27
Issue
1
Year of publication
1999
Pages
411 - 427
Database
ISI
SICI code
0092-7872(1999)27:1<411:SOLEEO>2.0.ZU;2-X
Abstract
In this paper we solve the algorithmic problem of recognizing the compatibi lity of a system of linear equations over a free associative algebra of the variety M-k defined by the identity [x(1), y(1)][x(2), y(x)] ... [x(k), y( k)] = 0, which is then used to prove that the free NcU-Lie algebras have th e solvable occurrence problem.