by Jordan, David A.

We study the algebra R

_p,q
generated by the Eulerian derivatives for two parameters p and q. Subject to certain conditions on the parameters, we show that R

_p,q
is a finitely presented N-graded algebra of Gelfand–Kirillov dimension 3. We establish a criterion for the cyclic module R

_p,q
/R

_p,q

f to be Noetherian, where f is homogeneous of degree 1. For some choices of the parameters, this criterion always holds and we know of no situation where it fails. It is not known whether R

_p,q
is Noetherian. We classify the point modules for R

_p,q
and determine the normal elements and graded automorphisms for R

_p,q
.

DOI: 10.1023/A:1011481028760
Print publication date: 8/1/2001
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by Lorenz, Martin

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.

DOI: 10.1023/A:1011415025465
Print publication date: 8/1/2001
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by Artamonov, Vyacheslav A.; Wisbauer, Robert

We study the endomorphim semigroup of a general quantum polynomial ring, its finite groups of automorphisms, and homological properties, as a module over the skew group ring of a finite group of automorphisms. Moreover, properties of the division ring of fractions are considered.

DOI: 10.1023/A:1011458821831
Print publication date: 8/1/2001
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by Natale, Sonia

We obtain further classification results for semisimple Hopf algebras of dimension pq
² over an algebraically closed field k of characteristic zero. We complete the classification of semisimple Hopf algebras of dimension 28.

DOI: 10.1023/A:1011434104084
Print publication date: 8/1/2001
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by Bueso, José L.; Gómez-Torrecillas, J.; Lobillo, F. J.

In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Ext
ⁱ
(M,N) is provided when N is a centralizing bimodule.

DOI: 10.1023/A:1011455831400
Print publication date: 8/1/2001
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