GENERIC EXTENSIONS AND MULTIPLICATIVE BASES OF QUANTUM GROUPS AT q = 0
نویسنده
چکیده
We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at q = 0 of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multiplicative basis is related to Lusztig’s canonical basis.
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