摘要:

According to a theorem of Masbaum and Wenzl [11], the Turaev-Viro invariant of a 3-manifold associated with the modular categories constructed fromUqslNis a cyclotomic integer whenqis of prime order. We extend this result to premodular categories (where theS-matrix need not be invertible) of 'type A of a more general kind.

ISSN:0092-7872    

DOI:10.1080/00927870008826941

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826942

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We study the injective comodules for the coordinate bialgebra of quantum 2 × 2 matrices at a root of unity. The relatedGL2andSL2theories are also specified.

ISSN:0092-7872    

DOI:10.1080/00927870008826943

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetG=Zpbe a cyclic group of prime orderpwith a representationG→GL(V) over a fieldKof characteristicp. In 1976, Almkvist and Fossum gave formulas for the decomposition of the symmetric powers ofVin the case thatVis indecomposable. From these they derived formulas for the Hilbert series of the invariant ringK[V]G. Following Almkvist and Fossum in broad outline, we start by giving a shorter, self-contained proof of their results. We extend their work to modules which are not necessarily indecomposable. We also obtain formulas which give generating functions encoding the decompositions of all symmetric powers ofVinto indecomposables. Our results generalize to groups of the typeZp×Hwith |H| coprime top. Moreover, we prove that for any finite groupGwhose order is divisible bypbut not byp2the invariant ringA,K[V]Gis generated by homogeneous invariants of degrees at most dim (V).(|G| – 1).

ISSN:0092-7872    

DOI:10.1080/00927870008826944

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826945

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this note we introduce the notion of 1-complete arrangements of ideals, and, taking into account an arrangement of prime divisors of a radical principal ideal, we give a sufficient condition for a noetherian local domain to be normal.

ISSN:0092-7872    

DOI:10.1080/00927870008826946

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this work we consider primitive sharp permutation groups of type ({0,l}, n). According to a previous result of the author, either the structure of such a group (as well as the associated action) is completely determined, or the group is almost simple. We investigate the viability of the almost simple case, develope additional restrictions on the structure of one point stabilizers, and give some indication of a strategy for a proof that there are no almost simple, primitive sharp permutation groups of type ({0l}n).

ISSN:0092-7872    

DOI:10.1080/00927870008826947

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

A triple system is partially associative (by definition) if it satisfies the identity (abc)de + a(bcd)e + ab(cde) ≡ 0. This paper presents a computational study of the free partially associative triple system on one generator with coefficients in the ring Z of integers. In particular, the Z-module structure of the homogeneous submodules of (odd) degrees ≤ 11 is determined, together with explicit generators for the free and torsion components in degrees ≤ 9. Elements of additive order 2 exist in degrees ≥ 7, and elements of additive order 6 exist in degrees ≥ 9. The most difficult case (degree 11) requires finding the row-reduced form over Z of a matrix of size 364 × 273. These computations were done with Maple V.4 on a Sun workstation.

ISSN:0092-7872    

DOI:10.1080/00927870008826948

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Over an arbitrary ring, we consider cotilting modules endowed with some finiteness conditions. We show that they correspond to pairs of dualities between certain cat-egories consisting of finitely presented modules. This extends the Cotilting Theorem proved by Colby for the noetherian case. The relationship with the cotilting modules studied by Colpi, D'Este, Tonolo and Trlifaj is also discuss.d.

ISSN:0092-7872    

DOI:10.1080/00927870008826949

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We study the homogeneous spaces of a smooth group G over affine spaces or local k-algebra and gerbs locally banded by a semi-simple group H dèfine over k. In particular we show that every gerb locally banded by H and rationally trivial is trivial, and that an homogeneous space of G with semi-simple isotropy which is rationally trivial is trivial in the Zariski topology. This extends a result of Colliot-Thélène and Ojanguren concerning G-torsors.

ISSN:0092-7872    

DOI:10.1080/00927870008826950

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor