by Abuhlail, Jawad Y.

In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi–Koppinen structures and dual Doi–Koppinen modules introduced (in the infinite case over rings) by the author in his dissertation.

DOI: 10.1007/s10468-005-3605-4
Print publication date: 5/1/2005
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by SmalØ, S. O.; Valenta, A.

Let Λ be a finitely generated associative k-algebra where k is an algebraically closed field. For each natural number d, we have the variety of d-dimensional module structures on kd given by the multiplication of the elements from a generating set of Λ. The general linear group Gld(k) acts on this variety by conjugation and the orbits under this action correspond to isomorphism classes of d-dimensional Λ-modules. For two d-dimensional Λ-modules M and N one says that M degenerates to N if the orbit corresponding to N is in the Zariski-closure of the orbit corresponding to M. Now in this situation the stabilizers of the elements in the orbit corresponding to N acts on the orbit corresponding to M.

In this paper we characterize degenerations of k[t]/(tr)-modules with the property that for each y in the orbit corresponding to N, there is an xy in the orbit corresponding to M such that the orbit corresponding to M is the disjoint union of orbits of the xy’s under the action of the stabilizer of y where y runs through the orbit corresponding to N.

DOI: 10.1007/s10468-005-3604-5
Print publication date: 5/1/2005
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by Barnea, Yiftach

Let
$\mathfrak{g}$
be a central simple Lie algebra over a field
$\mathbb{F}$
. We study the maximal ℤn-graded subalgebra of
$\mathfrak{g}\otimes_{\mathbb{F}}\mathbb{F}[x_{1},x_{1}^{-1},\ldots,x_{n},x_{n}^{-1}]$
.

DOI: 10.1007/s10468-005-3597-0
Print publication date: 5/1/2005
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by Happel, Dieter; Unger, Luise

DOI: 10.1007/s10468-005-3595-2
Print publication date: 5/1/2005
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by Lichtman, A. I.

Let D be an arbitrary skew field and K a central subfield of D. We prove that D can be embedded in a skew field Δ such that w(Δ)=Δ for every nonempty Lie word w on a set of variables y1,y2,. . . with coefficients in K; moreover, we have for the multiplicative group Δ* that v(Δ*)=Δ* for every nonempty word
$v=x_{1}^{\varepsilon_{1}}x_{2}^{\varepsilon_{2}}\ldots x_{n}^{\varepsilon_{n}}$
(ɛi=±1; i=1,2,. . .,n).

DOI: 10.1007/s10468-005-3570-y
Print publication date: 5/1/2005
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by Caenepeel, S.; Zhu, Bin

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another: contravariant finiteness of the subcategory of (finitely generated) left modules with finite projective dimension, finitistic dimension, finite representation type, Auslander algebra, tame or wild representation type.

DOI: 10.1007/s10468-005-0971-x
Print publication date: 5/1/2005
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by Drozd, Yuriy A.

We prove that the number of parameters defining a complex of projective modules over an algebra is upper semi-continuous in families of algebras. The proof follows the pattern of the paper by Drozd and Greuel and rests upon universal families with projective bases. Supposing that every algebra is either derived tame or derived wild, we get that a degeneration of a derived wild algebra is also derived wild. We also discuss an apparent counter-example to the last assertion by Th. Brüstle.

DOI: 10.1007/s10468-005-0967-6
Print publication date: 5/1/2005
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by Gnedin, Alexander; Kerov, Sergey

We focus on derangement characters of GL(n,q) which depend solely on the dimension of the space of fixed vectors. This family includes Thoma characters which become asymptotically irreducible as n→∞. We find explicit decomposition of Thoma characters into irreducibles, construct further derangement characters and seek for extremes in the family derangement characters.

DOI: 10.1007/s10468-005-0858-x
Print publication date: 5/1/2005
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by Cox, Ben L.

This work expands to the setting of
$\widehat{\mathfrak{sl}_{n}(\mathbb{C})}$
the results of H. Jakobsen and V. Kac and independently D. Bernard and G. Felder on the realization of
$\widehat{\mathfrak{sl}_{2}(\mathbb{C})}$
, in terms of infinite sums of partial differential operators. We note in the paper that, in the generic case, these geometric constructions are just realizations of the imaginary Verma modules studied by V. Futorny.

DOI: 10.1007/s10468-005-0857-y
Print publication date: 5/1/2005
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by Leuschke, Graham J.; Wiegand, Roger

Let
$(R,\mathfrak{m},k)$
be a complete local Cohen–Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field). In the first section we deal with the complete case, and in the second we show that bounded CM type ascends to and descends from the completion. In the third section we study ascent and descent in higher dimensions and prove a Brauer–Thrall theorem for excellent rings.

DOI: 10.1007/s10468-004-8319-5
Print publication date: 5/1/2005
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