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Let k be an algebraically closed field. It is known that any stable equivalence between standard representation-finite self-injective k-algebras (without blocks of Lowey length 2) lifts to a standard derived equivalence, in particular, it is of Morita type. In this note, we show that the same holds for any stable equivalence between nonstandard representation-finite self-injective k-algebras. This settles an open question raised by H. Asashiba about twenty years ago.
We review Morita equivalence for finite type $k$-algebras $A$ and also a weakening of Morita equivalence which we call stratified equivalence. The spectrum of $A$ is the set of equivalence classes of irreducible $A$-modules. For any finite type $k$-a
We give a short proof based on Lusztigs generalized Springer correspondence of some results of [BrCh,BaCr,P].
In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal character sheaves. Irreducible representations of Hecke algebras associated to complex reflection groups at roots
We formulate a Satake isomorphism for the integral spherical Hecke algebra of an unramified $p$-adic group $G$ and generalize the formulation to give a description of the Hecke algebra $H_G(V)$ of weight $V$, where $V$ is a lattice in an irreducible algebraic representation of $G$.
We introduce a Morita type equivalence: two operator algebras $A$ and $B$ are called strongly $Delta $-equivalent if they have completely isometric representations $alpha $ and $beta $ respectively and there exists a ternary ring of operators $M$ suc