SLn(F [x]) Is Not Boundedly Generated by Elementary Matrices: Explicit Proof

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Igor Erovenko, Associate Professor and Director of Undergraduate Study (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: Using methods of higher algebraic K-theory, van der Kallen proved that SLn(F [x]) does not have bounded word length with respect to elementary matrices if the field F has infinite transcendence degree over its prime subfield. We exhibit a short explicit proof of this result by constructing a sequence of matrices with infinitely growing word length. We also use this construction to show that SLn(Z[x]) does not have bounded word length with respect to elementary matrices of “bounded degree”.

Additional Information

Publication
Electronic Journal of Linear Algebra (2004) 11, 162-167 (electronic)
Language: English
Date: 2004

Email this document to