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Abstract
An element it of a finitely generated free Lie algebra L is a test element if any endomorphism of L fixing u is an automorphism. We prove that test elements of L are precisely those elements not contained in any proper retract of L. In addition we characterize retracts of free Lie algebras.
†Partially supported by RFBR and by INTAS.
‡t1n 1996/1997 on leave as a Rayson Iluang I'osldoctoral Fellow at the Robert Black College, the University of IIong Kong.
§Patially supported by RGC Fundable Crarit 341/021/0001 and CRCG Grant 337/O24/OOOl.
†Partially supported by RFBR and by INTAS.
‡t1n 1996/1997 on leave as a Rayson Iluang I'osldoctoral Fellow at the Robert Black College, the University of IIong Kong.
§Patially supported by RGC Fundable Crarit 341/021/0001 and CRCG Grant 337/O24/OOOl.
Notes
†Partially supported by RFBR and by INTAS.
‡t1n 1996/1997 on leave as a Rayson Iluang I'osldoctoral Fellow at the Robert Black College, the University of IIong Kong.
§Patially supported by RGC Fundable Crarit 341/021/0001 and CRCG Grant 337/O24/OOOl.