3,830 research outputs found
On cubic functors
We prove that the description of cubic functors is a wild problem in the
sense of the representation theory. On the contrary, we describe several
special classes of such functors (2-divisible, weakly alternative, vector
spaces and torsion free ones). We also prove that cubic functors can be defined
locally and obtain corollaries about their projective dimensions and torsion
free parts.Comment: 24 page
On K_0 of locally finte categories
We calculate the Grothendieck group , where is an
additive category, locally finite over a Dedekind ring and satisfying some
additional conditions. The main examples are categories of modules over finite
algebras and the stable homotopy category of finite CW-complexes.
We show that this group is a direct sum of a free group arising from
localizations of the category and a group analogous to the groups of
ideal classes of maximal orders. As a corollary, we obtain a new simple proof
of the Freyd's theorem describing the group .Comment: 21 page
Derived tame and derived wild algebras
We prove that every finite dimensional algebra over an algebraically closed
field is either derived tame or derived wild. We also prove that any
deformation of a derived tame algebra is derived tame.Comment: 15 page
Locally finite simple weight modules over twisted generalized Weyl algebras
We present methods and explicit formulas for describing simple weight modules
over twisted generalized Weyl algebras. When a certain commutative subalgebra
is finitely generated over an algebraically closed field we obtain a
classification of a class of locally finite simple weight modules as those
induced from simple modules over a subalgebra isomorphic to a tensor product of
noncommutative tori. As an application we describe simple weight modules over
the quantized Weyl algebra.Comment: 28 page
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