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2000 Mathematics Subject Classification: 16R10, 16R20, 16R50The algebra Mn(K) of the matrices n × n over a field K can be regarded as a Z-graded algebra. In this paper, it is proved that if K is an
infinite field, all the Z-graded polynomial identities of Mn(K) follow from the identities:
x = 0, |α(x)| ≥ n,
xy = yx, α(x) = α(y) = 0,
xyz = zyx, α(x) = −α(y) = α(z ),
where α is the degree of the corresponding variable.
This is a generalization of a result of Vasilovsky about the Z-graded identities...
Sullivan associated a uniquely determined to any simply connected simplicial complex . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space . In case is the total space of a principal -bundle, ( is a compact connected Lie-group) we associate a -equivariant model , which is a collection of “-homotopic” ’s with -action. will, in general, be different from the Sullivan’s minimal model of the space . contains the total rational...
We show that there are exactly three types of Hilbert series of Artin-Schelter regular algebras of dimension five with two generators. One of these cases (the most extreme) may not be realized by an enveloping algebra of a graded Lie algebra. This is a new phenomenon compared to lower dimensions, where all resolution types may be realized by such enveloping algebras.
We recall the notion of Hopf quasigroups introduced previously by the authors. We construct a bicrossproduct Hopf quasigroup from every group with a finite subgroup and IP quasigroup transversal subject to certain conditions. We identify the octonions quasigroup as transversal in an order 128 group with subgroup and hence obtain a Hopf quasigroup as a particular case of our construction.
On définit une structure de bigèbre différentielle graduée sur la somme directe des complexes cellulaires des permutoèdres, qui contient une sous-bigèbre différentielle graduée dont le complexe sous-jacent est la somme directe des complexes cellulaires des polytopes de Stasheff. Ceci étend des constructions de Malvenuto et Reutenauer et de Loday et Ronco pour les sommets des mêmes polytopes.
Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.
Let and be two pointed sets. Given a family of three maps , this family provides an adequate decomposition of as the orthogonal disjoint union of well-described -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak -algebras.
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