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Let be a semisimple complex algebraic group and its flag variety. Let and let be its enveloping algebra. Let be a Cartan subalgebra of . For , let be the corresponding minimal primitive ideal, let , and let be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the -algebras . When is regular, Hodges has shown that . In this case is generated by the classes corresponding to...
Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group , endowed with the Euler form, and its automorphism group on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group of the derived category of Λ.
This paper is motivated by the question whether there is a nice structure theory
of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, of a -adic analytic group . For without any -torsion element we prove that is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null -module. This is classical when for some integer , but was previously unknown in the non-commutative case. Then the category of -modules...
The aim of this note is to give an affirmative answer to a problem raised in [9] by J. Nehring and A. Skowroński, concerning the number of nonstable ℙ₁(K)-families of quasi-tubes in the Auslander-Reiten quivers of the trivial extensions of tubular algebras over algebraically closed fields K.
We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].
We introduce the right (left) Gorenstein subcategory relative to an additive subcategory of an abelian category , and prove that the right Gorenstein subcategory is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When is self-orthogonal, we give a characterization for objects in , and prove that any object in with finite -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in with finite -projective dimension...
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