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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.
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