. Q A ] 2 7 O ct 2 00 6 A GENERALIZATION OF COXETER GROUPS , ROOT SYSTEMS , AND MATSUMOTO ’ S THEOREM
نویسنده
چکیده
The root systems appearing in the theory of Lie superalgebras and Nichols algebras admit a large symmetry extending properly the one coming from the Weyl group. Based on this observation we set up a general framework in which the symmetry object is a groupoid. We prove that in our context the groupoid is generated by reflections and Coxeter relations. This answers a question of Serganova. Our weak version of the exchange condition allows us to prove Matsumoto’s theorem. Therefore the word problem is solved for the groupoid.
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تاریخ انتشار 2006