38 research outputs found
Glider representations of group algebra filtrations of nilpotent groups
We continue the study of glider representations of finite groups with
given structure chain of subgroups . We give a characterization of irreducible gliders of essential length which in the case of -groups allows to prove some results about
classical representation theory. The paper also contains an introduction to
generalized character theory for glider representations and an extension of the
decomposition groups in the Clifford theory. Furthermore, we study irreducible
glider representations for finite nilpotent groups.Comment: 18 pages Erratum fixed: the result in Corollary 3.17 is only valid
for H a maximal normal subgrou
PBW deformations of Koszul algebras over a nonsemisimple ring
Let be a generalized Koszul algebra over a finite dimensional algebra
. We construct a bimodule Koszul resolution of when the projective
dimension of equals 2. Using this we prove a Poincar\'e-Birkhoff-Witt
(PBW) type theorem for a deformation of a generalized Koszul algebra. When the
projective dimension of is greater than 2, we construct bimodule Koszul
resolutions for generalized smash product algebras obtained from braidings
between finite dimensional algebras and Koszul algebras, and then prove the PBW
type theorem. The results obtained can be applied to standard Koszul
Artin-Schelter Gorenstein algebras in the sense of Minamoto and Mori.Comment: Section 3 revised, to appear in Math.
Nakayama automorphisms of double Ore extensions of Koszul regular algebras
Let be a Koszul Artin-Schelter regular algebra and an algebra
homomorphism from to . We compute the Nakayama
automorphisms of a trimmed double Ore extension
(introduced in \cite{ZZ08}). Using a similar method, we also obtain the
Nakayama automorphism of a skew polynomial extension , where
is a graded algebra automorphism of . These lead to a
characterization of the Calabi-Yau property of , the
skew Laurent extension and with a diagonal type.Comment: The paper has been heavily revised including the title, and will
appear in Manuscripta Mathematic