Finite Dimensional Algebras, Quantum Groups and Finite Groups of Lie Type
نویسنده
چکیده
We shall discuss generic extension monoids associated with finite dimensional (basic) hereditary algebras of finite or cyclic type and related applications to Ringel–Hall algebras, (and hence, to quantum groups). We shall briefly review the geometric setting of quantum gln by Beilinson, Lusztig and MacPherson and its connections to Ringel– Hall algebras and q-Schur algebras. In the second part of the paper, we shall survey the development of stratified algebras and their applications to the (generalized) q-Schur algebra of finite groups of Lie type.
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