by Skowroński, Andrzej; Yamagata, Kunio

We prove new results on the stable equivalences of selfinjective Artin algebras of tilted Dynkin type, extending the main results of Skowroński and Yamagata to arbitrary tilted type.

DOI: 10.1007/s10468-005-9005-y
Online Date: 4/22/2006
Print publication date: 2/1/2006
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by Nishida, Kenji

We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k.

DOI: 10.1007/s10468-005-9004-z
Online Date: 4/19/2006
Print publication date: 2/1/2006
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by Marko, František; Zubkov, Alexandr N.

The structure of a Schur superalgebra S = S(1 ∣ 1, r) in odd characteristic p is completely determined. The algebra S is semisimple if and only if p does not divide r. If p divides r, then simple S-modules are one-dimensional and the quiver and relations of S can be immediately seen from its regular representation computed in this paper. Surprisingly, if p divides r, then S is neither quasi-hereditary nor cellular nor stratified, as one would expect by analogy with classical Schur algebras or Schur superalgebras in characteristc zero.

DOI: 10.1007/s10468-005-9001-2
Online Date: 4/19/2006
Print publication date: 2/1/2006
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by Popescu, Nicolae; Vâjâitu, Marian; Zaharescu, Alexandru

Let T be a transcendental element of
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
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% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq
% WIceYOdaWgaaWcbaGaamiCaaqabaaaaa!3A08!$$\mathbb{C}_p
$$ and
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca
% qGpbWaaeWaaeaacaWGubaacaGLOaGaayzkaaGaeyypa0ZaaiWaaeaa
% cqaHdpWCdaqadaqaaiaadsfaaiaawIcacaGLPaaacaGG6aGaeq4Wdm
% NaeyicI4Saae4raiaabggacaqGSbWaaSbaaSqaaiaabogacaqGVbGa
% aeOBaiaabshaaeqaaOWaaeWaaeaadaWcgaqaaiablkqiJoaaBaaale
% aacaWGWbaabeaaaOqaaiablQriKoaaBaaaleaacaWGWbaabeaaaaaa
% kiaawIcacaGLPaaaaiaawUhacaGL9baaaaa!5374!
$$
{\text{O}}{\left( T \right)} = {\left\{ {\sigma {\left( T \right)}:\sigma \in {\text{Gal}}_{{{\text{cont}}}} {\left( {{\mathbb{C}_{p} } \mathord{\left/
{\vphantom {{\mathbb{C}_{p} } {\mathbb{Q}_{p} }}} \right.
\kern-\nulldelimiterspace} {\mathbb{Q}_{p} }} \right)}} \right\}}
$$ the orbit of T. On
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% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca
% qGpbWaaeWaaeaacaWGubaacaGLOaGaayzkaaaaaa!3AC4!
$$
{\text{O}}{\left( T \right)}
$$we have a Haar measure
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq
% aHapaCdaqadaqaaiaadsfaaiaawIcacaGLPaaaaaa!3BAF!$$\pi \left( T \right)$$. The goal of this paper is to characterize all the elements of
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq
% WIceYOdaWgaaWcbaGaamiCaaqabaaaaa!3A08!$$\mathbb{C}_p$$ for which the integral
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca
% qGubGaaeOCamaabmaabaGaamivaaGaayjkaiaawMcaaiaacQdacqGH
% 9aqpdaWdXaqaaiaadQhacaqGKbGaeqiWda3aaSbaaSqaaiaadshaae
% qaaOWaaeWaaeaacaWG6baacaGLOaGaayzkaaaaleaacaqGpbWaaeWa
% aeaacaWGubaacaGLOaGaayzkaaaabaaaniabgUIiYdaaaa!4A39!
$$
{\text{Tr}}{\left( T \right)}: = {\int_{{\text{O}}{\left( T \right)}}^{} {z{\text{d}}\pi _{t} {\left( z \right)}} }
$$, called the trace of T, is well defined.

DOI: 10.1007/s10468-005-9003-0
Online Date: 4/19/2006
Print publication date: 2/1/2006
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by Berger, Roland; Marconnet, Nicolas

The Koszul property was generalized to homogeneous algebras of degree $$N>2$$ in [5], and related to $$N$$-complexes. We show that if the $$N$$-homogeneous algebra $$A$$ is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem to $$A$$ i.e., there is a Poincaré duality between Hochschild homology and cohomology of $$A$$ as for $$N = 2$$.

DOI: 10.1007/s10468-005-9002-1
Online Date: 4/8/2006
Print publication date: 2/1/2006
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by Petit, Toukaiddine; Oystaeyen, Freddy

We consider filtered or graded algebras A over a field K. Assume that there is a discrete valuation Ov of K with mv its maximal ideal and kv:=Ov/mv its residue field. Let Λ be Ov-order such that ΛK=A and
$\overline{\Lambda}:=k_{v}\otimes_{O_{v}}\Lambda$
the Λ-reduction of A at the place
$K\leadsto k_{v}$
. As in many examples of quantized algebras A comes with a specific filtration that reduces well with respect to the valuation filtration defined by Λ on A and the reduction relates to the part of degree zero in the associated graded algebra. Hence several lifting properties fellow from valuation like theory, also for modules with good filtrations.

DOI: 10.1007/s10468-005-8761-z
Print publication date: 4/1/2006
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by Gubareni, N. M.; Kirichenko, V. V.

In this paper we consider serial rings with T-nilpotent prime radical, factor-rings of which by the prime radical are right Noetherian rings. We prove that the prime quiver of such a ring is a disconnected union of cycles and chains. In the case when the prime quiver of such a serial ring is a chain the prime radical is nilpotent. For serial rings with nilpotent prime radical we introduce an analogue of Kupisch series.

DOI: 10.1007/s10468-005-8759-6
Print publication date: 4/1/2006
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by Savage, Alistair

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type An(1), we extend the Young wall construction to arbitrary level, describing a combinatorial realization of the crystals in terms of new objects which we call Young pyramids.

DOI: 10.1007/s10468-005-0565-7
Print publication date: 4/1/2006
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by Hajac, Piotr M.; Matthes, Rainer; Szymanski, Wojciech

The irreducible *-representations of the polynomial algebra
$\mathcal{O}(S^{3}_{pq})$
of the quantum3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C*-algebra are shown to coincide with their classical counterparts. The U(1)-action on
$\mathcal{O}(S^{3}_{pq})$
corresponding for p=1=q to the classical Hopf fibration is proven to be Galois (free). The thus obtained locally trivial Hopf–Galois extension is shown to be equivariantly projective (admitting a strong connection) and non-cleft. The latter is proven by determining an appropriate pairing of cyclic cohomology and K-theory.

DOI: 10.1007/s10468-005-3080-y
Print publication date: 4/1/2006
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by Jorgensen, David A.; Şega, Liana M.

We show that the conditions defining total reflexivity for modules are independent. In particular, we construct a commutative Noetherian local ring R and a reflexive R-module M such that ExtRi(M,R)=0 for all i>0, but ExtRi(M*,R)≠0 for all i>0.

DOI: 10.1007/s10468-005-0559-5
Print publication date: 4/1/2006
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