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A Basis for Z-Graded Identities of Matrices over Infinite Fields

Azevedo, Sergio (2003)

Serdica Mathematical Journal

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...

A $G$ -minimal model for principal $G$ -bundles

Shrawan Kumar (1982)

Annales de l'institut Fourier

Sullivan associated a uniquely determined $D G A |_{Q}$ to any simply connected simplicial complex $E$ . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space $E$ . In case $E$ is the total space of a principal $G$ -bundle, ( $G$ is a compact connected Lie-group) we associate a $G$ -equivariant model $U_{G} [E]$ , which is a collection of “ $G$ -homotopic” $D G A$ ’s $|_{R}$ with $G$ -action. $U_{G} [E]$ will, in general, be different from the Sullivan’s minimal model of the space $E$ . $U_{G} [E]$ contains the total rational...

A Remark on tilting theory and DG algebras.

Bernhard Keller (1993)

Manuscripta mathematica

A structure sheaf on the projective spectrum of a graded fully bounded Noetherian ring.

Samir Mahmoud, S. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Aktionen kompakter Liegruppen auf lokalen Räumen.

Volker Hauschild (1979)

Mathematische Zeitschrift

Algèbre des descentes et cogroupes dans les algèbres sur une opérade

Benoît Fresse (1998)

Bulletin de la Société Mathématique de France

Algèbres graduées normales II - Construction d’un schéma sur certains anneaux $ℕ^{n}$ -gradués

Philippe Carbonne (1985)

Publications mathématiques et informatique de Rennes

Appendix to "On the double Poincaré series of the enveloping algebras of certain graded Lie algebras".

Clas Löfwall (1982)

Mathematica Scandinavica

Applications of epigroups to graded ring theory.

A.V. Kelarev (1995)

Semigroup forum

Artin-Schelter regular algebras of dimension five

Gunnar Fløystad, Jon Eivind Vatne (2011)

Banach Center Publications

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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