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Journal of the London Mathematical Society 2005 72(1):137-150; doi:10.1112/S0024610705006526
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© The London Mathematical Society

The Composition Algebra and the Composition Monoid of the Kronecker Quiver

Andrew Hubery

Institut für Mathematik, Universität Paderborn Warburger Strasse 100, 33098 Paderborn, Germany hubery{at}math.upb.de

Received 19 April 2004. Revision received 9 September 2004.

The Kronecker quiver K is considered, and the relations for the specialisation at q = 0 of the generic composition algebra are given, as well as those for Reineke's composition monoid. As a corollary, it is deduced that the composition monoid is a proper factor of the specialisation of the composition algebra. A normal form is also obtained for the varieties occurring in the composition monoid in terms of Schur roots.


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